What does Macbeth's soliloquy in act 3, scene 1, beginning with "To be thus is nothing; but to be safely thus," mean?

Macbeth is saying that now that he is king, he finds that it is more difficult to maintain his kingship than he imagined it would be: "To be thus is nothing;/But to be safely thus.--". Now that he's king, what he's focusing on is the fact that he does not feel safe in this position, especially because of Banquo's depth of understanding.

In part, this is because of his guilty conscience - the fact that not only has he committed regicide (killed the king) to gain the throne, but also he does not have the right to claim the kingship. Duncan had named his successor (Malcolm) before his death, as he was entitled to do, and Shakespeare's audience believed the kingship was bestowed by God. So Macbeth was not entitled to the kingship on either count.

Also, because of his own treachery, he distrusts other people, who may betray him. And he especially fears Banquo, who heard what the witches said, and who also was told his sons would succeed to the throne. Macbeth is now obsessing about the fact that he has damned himself to hell to attain the crown, and it won't even stay in his own family's hands.

At the end of the speech we see that he has already decided to take matters into his own hands again - he has a plan to kill Banquo and his son.

What does Macbeth's soliloquy in act 3, scene 1, beginning with "To be thus is nothing; but to be safely thus," mean?

Macbeth has become king as he aspired, but he fears that he is not safe as long as Banquo is alive. Banquo heard the prophesies of the witches and Macbeth thinks Banquo knows the king was murdered. He also talks about how the witches said Macbeth would be king, but they said Banquo would be father to kings, which would be considered better. At the end of the soliloquy, Macbeth realizes that if Banquo's sons are going to be the future kings, then Macbeth has committed murder for him. Macbeth benefits little from it.

Why is Macbeth's "To be thus is nothing" soliloquy in act 3, scene 1 significant to the overall play?

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In Macbeth, this soliloquy in Act III, scene i develops Macbeth's character as his "vaulting ambition"  (I.vii.27) takes over from all reason. From deciding against even killing Duncan "We will proceed no further in this business"(30), Macbeth is now intent on removing anyone who may prevent him from becoming king. Macbeth is lamenting the possibility that Banquo's sons may take the throne as the witches "hail'd him father to a line of kings."(III.i 59) This would mean that "For them the gracious Duncan have I murder'd."(65) 

Macbeth's words also develop the plot as Macbeth, who initially depended on Lady Macbeth's harsh talking and her casting aspersions on his manhood when she suggested,"When you durst do it, then you were a man," (I.vii.49) becomes more determined to attain and retain the crown. He is now king and knows that Banquo thinks "thou play'dst most foully for't"(III.i.3) and, even without Lady Macbeth's urging, believes he is invincible. His fear drives him and he intends to have Banquo murdered. Importantly, the audience notes Lady Macbeth's exclusion from his decision to kill Banquo. This will become relevant as her guilt will lead to her ultimate madness and death.  

What does the quote "To be thus is nothing, but to be safely thus" from Macbeth mean?

"To be thus is nothing, but to be safely thus-- Our fears in Banquo stick deep, And in his royalty of nature reigns that Which would be feared. 'Tis much he dares; And to that dauntless temper of his mind He hath a wisdom that doth guide his valour To act in safety. There is none but he Whose being I do fear; and under him My genius is rebuked, as it is said, Marc Antony's was by Caesar."

Macbeth is referring to Marc Antony and Octavius Caesar when he talks about fearing Banquo and feeling inferior to him. This simile derives from Plutarch. Shakespeare elaborated on it in his play Antony and Cleopatra in Act 2, Scene 3, in which the Egyptian soothsayer advises Antony to return to Egypt. This is probably good advice.

     Soothsayer.
    Therefore, O Antony, stay not by his side:
    Thy demon, that's thy spirit which keeps thee, is
    Noble, courageous high, unmatchable,
    Where Caesar's is not; but, near him, thy angel
    Becomes a fear, as being o'erpower'd: therefore
    Make space enough between you.

    Antony. Speak this no more.

    Soothsayer. To none but thee; no more, but when to thee.
    If thou dost play with him at any game,
    Thou art sure to lose; and, of that natural luck,
    He beats thee 'gainst the odds: thy lustre thickens,
    When he shines by: I say again, thy spirit
    Is all afraid to govern thee near him;
    But, he away, 'tis noble.

    Antony. Get thee gone:
    Say to Ventidius I would speak with him:
    [Exit Soothsayer]
    He shall to Parthia. Be it art or hap,
    He hath spoken true: the very dice obey him;
    And in our sports my better cunning faints
    Under his chance: if we draw lots, he speeds;
    His cocks do win the battle still of mine,
    When it is all to nought; and his quails ever
    Beat mine, inhoop'd, at odds. I will to Egypt:
    And though I make this marriage for my peace,
    I' the east my pleasure lies.

Antony and Octavius are two quite different types. Antony is depicted as sensual, hedonistic, athletic, but improvident and reckless. Octavius is depicted as sober, calculating, cunning, and highly intelligent. In any contest between these two men, Octavius seems likely to win. In Jungian terms, Antony might be described as an extravert whose principal conscious function is sensation, while Octavius might be described as an introvert who principal conscious function is thinking. Naturally Octavius would be much better at planning, as is seen in the outcome of the rivalry between the two in Shakespeare's Antony and Cleopatra.

In Jungian terms, Banquo might also be described as an intellectual and introvert whose principal conscious function is thinking, while Macbeth might be described as an athletic extravert whose principal conscious function is sensation (physical action). Macbeth has good reason to be afraid of him, especially since the three witches have warned Macbeth that Banquo's descendants, not Macbeth's, will inherit the throne.

What does the quote "To be thus is nothing, but to be safely thus" from Macbeth mean?

"To be thus is nothing, but to be safely thus-- Our fears in Banquo stick deep, And in his royalty of nature reigns that Which would be feared. 'Tis much he dares; And to that dauntless temper of his mind He hath a wisdom that doth guide his valour To act in safety. There is none but he Whose being I do fear; and under him My genius is rebuked, as it is said, Marc Antony's was by Caesar."

The following excerpt is from Shakespeare's play "Antony and Cleopatra." It shows what Macbeth is referring to when he compares himself and Banquo to Antony and Octavius Caesar, saying, ". . . and under him / My genius is rebuked, as it is said / Mark Antony's was by Caesar."

Antony                                          Say to me,
Whose fortunes shall rise higher, Caesar's or mine?

Soothsayer   Caesar's.
Therefore, O Antony! Stay not by his side;
Thy demon--that's thy spirit which keeps thee,--is
Noble, courageous, high, unmatchable,
Where Caesar's is not; but near him thy angel
Becomes a fear, a being o'erpower'd; therefore
Make space enough between you.

Antony   Speak this no more.

Soothsayer   To none but thee; no more but when to thee.
If thou dost play with him at any game
Thou art sure to lose, and, of that natural luck,
He beats thee 'gainst the odds; thy lustre thickens
When he shines by. I say again, thy spirit
Is all afraid to govern thee near him,
But he away, 'tis noble.

Antony    Get thee gone;
Say to Ventidius I would speak with him.
[Exit Soothsayer]
He shall to Parthia. Be it art or hap
He hath spoken true; the very dice obey him.
And in our sports my better cunning faints
Under his chance; if we draw lots he speeds,
His cocks do win the battle still of mine
When it is all to nought, and his quails ever
Beat mine, inhoop'd, at odds.

Shakespeare derived his invaluable words of practical worldly wisdom from Plutarch. We will all find in our own lives that there are some individuals who seem to have the same effect on us that Octavius has on Antony. They make us feel awkward and inferior, although we are well aware that they are often actually inferior to us in many ways. As the Soothsayer tells Antony:

Thy demon--that's thy spirit which keeps thee,--is
Noble, courageous, high, unmatchable,
Where Caesar's is not . . .

The Soothsayer advises Antony to listen to his own feelings and be warned by them to stay as far away from Octavius as possible. We all meet lots of people in our lifetimes, and some of them are helpful while others are "takers" and "users" and can be dangerous. We need to become aware of our feelings and intuitions and to avoid the people who leave us with unpleasant feelings or who leave us feeling somehow drained. Sometimes our first impressions of others are the best evidence we will ever have to judge them.

Here is another pertinent quote:

In the presence of some people we inevitably depart from ourselves: we are inaccurate, say things we do not feel, and talk nonsense. When we get home we are conscious that we have made fools of ourselves. Never go near these people.             -Mark Rutherford

What does Macbeth mean by "to be thus, is nothing; but to be safely thus" in Macbeth?

Macbeth is saying that being king is not enough unless he remains king, and he says this right after he kills Duncan and before he kills Banquo.

Banquo and Macbeth were friends and fellow captains in Duncan’s army.  All evidence points to the fact that they were friends, or at least that Banquo looked out for Macbeth’s interests and worried about him.

Banquo was there when Macbeth first heard the witches’ prophecies, so he knows what they are.  He knows that Banquo might be suspicious, because he heard the witches tell him he’d be king before Duncan was killed.  Banquo could ruin the whole plan.

’Tis much he dares,(55)

And, to that dauntless temper of his mind,

He hath a wisdom that doth guide his valor

To act in safety. (Act 3, Scene 1)

 But there’s another problem.  The prophecy also said that Banquo’s sons would be king.  This cannot be.  Macbeth does not want a “fruitless crown.”  He has to get rid of Banquo and his son.  Macbeth decides to hire murderers to take out both Banquo and his son Fleance.

Macbeth goes from not wanting to commit one murder to committing several.  He seems to get a taste for blood, but he realizes that he has not commit another murder to cover up the first one, and another, and another.

What can you conclude about Macbeth's state of mind from this quote?To be thus is nothing, But to be safely thus. Our fears in Banquo Stick deep, and in his royalty of nature Reigns that which would be feared

These lines occur in Act III of Shakespeare's Macbeth. In Act II, Macbeth killed King Duncan. Now that Macbeth has succeeded in taking the throne, he is suffering from paranoia. The cause of his paranoia is the part of the witches' prophecy that predicted that one of Banquo’s line would someday be king. This leads Macbeth to feel that, as long as Banquo and his son are alive, he is not safe. 

The quote reveals that being king is not enough for Macbeth, he must be king and be “safe.” Banquo is something to be “feared.”

As we can see, one act of violence leads to another.