(act 3, scene 1, lines 70–75)

Because he is so bitter about this prophecy, Macbeth decides to arrange for the father and son's murders, but the crime must take place far from his home this time so as not to draw suspicion onto himself. If Duncan is murdered at Macbeth's house and then Banquo and Fleance end up murdered at Macbeth's house, that will look pretty sketchy. To that end, Macbeth tries to get information about where Banquo travels and when so that he can make arrangements to have him killed far away. Then, by confirming that Banquo intends to be back before the banquet that night, Macbeth makes it seem as though he is expecting to see Banquo later on; this, too, seems designed to make Macbeth look innocent.

Macbeth needs to know, with some amount of certainty, the approximate time Banquo and Fleance will be returning to Macbeth's castle. Remember, Banquo and Fleance come under a surprise attack, so it is important (to Macbeth) that he arrange for the murderers to be in the right place at the right time. Most importantly, however, this sets up the transformation of Macbeth from a superstitious and somewhat impulsive killer (Duncan), to a calculating murderer. The murder of Duncan is much different than the murder of Banquo and Fleance. Macbeth slips further and further into the darkness as he plots the death of his closest friend, Banquo.

The questions Macbeth asks Banquo in Act III, scene i appear to be casual, as if Macbeth is only concerned that Banquo not miss that night's banquet. In fact, they are very pointed questions. He wants to know when Banquo is leaving the castle and how far he will be riding. This will give him an idea of when Banquo will be returning. Macbeth needs this information so that he can pass it along to the men he has employed to attack Banquo and his son Fleance on the road and murder them both.

After his conversation with Banquo, Macbeth meets with the murderers. He tells them the following:

Within this hour at most
I will advise you where to plant yourselves,
Acquaint you with the perfect spy o' th' time,
The moment on 't; for 't must be done tonight,
And something from the palace;

This suggests that Macbeth has a general idea as to where Banquo will be, but he wants to plan precisely where the attack should take place to ensure success and to make sure Banquo and his son are not murdered near Macbeth's castle. After he figures it out, he will get back to them in no more than an hour.

Macbeth is planning to kill Banquo and wants to make sure he knows where to send the murderers.

Macbeth is pretty convinced that Banquo is on to him.  Banquo knows as much about the witches’ prophecies as Macbeth does.  He was there when the witches told him he would be king.  He was also there when Duncan was murdered.  Macbeth fears that Banquo is suspicious.  He is. 

In a soliloquy, Banquo tells the audience that he is afraid that Macbeth got his kingship through evil means.  When he says “Thou hast it now” he is saying, “Macebth, you are king.”  He is not talking directly to Macbeth, of course.  He also says that Macbeth “play'dst most foully for't,” meaning he got to be king through despicable acts, in this case killing the king (Act 3, Scene 1). 

Banquo knows that Macbeth is dangerous though, and he does not let on.  When Macbeth tells him he wants to see him at the ball, Banquo pretends he has no suspicions and is ever-loyal.  He worries about what Macbeth would do if he thought Banquo knew what he had done. 

MACBETH
To-night we hold a solemn supper sir,
And I'll request your presence.
BANQUO
Let your highness
Command upon me; to the which my duties
Are with a most indissoluble tie
For ever knit. (Act 3, Scene 1) 

Macbeth casually asks Banquo if he is riding, and how far, and reminds him not to miss the feast.   Banquo complies, but he is wary.  Later, when he sees the murderers Macbeth has sent, he knows what is going on.  He is with his son Fleance, and he tells him to run.  Fleance is able to get away then, but Banquo is not that lucky. 

Later, Banquo does make the banquet.  He comes as a ghost!  Macbeth is horrified when he sees him, and while Lady Macbeth makes excuses for him the guests are still disturbed by his actions.  It is a sign of Macbeth’s guilt and mental decline.

On a practical level, Macbeth is interested in Banquo's travel plans because he is going to have him and his son, Fleance, killed while they are on the road. In act 1, the Weird Sisters tell Banquo that he will "get kings," though he will not be king himself, and Macbeth develops serious resentment of Banquo because Macbeth will not pass his throne on to his own heirs; his royal line will end with him. He says the following:

[They] hailed [Banquo] father to a line of kings.
Upon my head they placed a fruitless crown
And put a barren scepter in my grip,
Thence to be wrenched with an unlineal hand,
No son of mine succeeding. If 't be so,
For Banquo's issue have I filed my mind (3.1.65–70).

In other words, Macbeth is angry because he feels that he has ruined his own peace of mind to gain the throne, and Banquo's line will reap the benefits of his actions.

In addition to Macbeth's desire to get rid of Banquo and his son so that they will no longer pose a threat, Lady Macbeth's advice to Macbeth before killing King Duncan provides another reason for Macbeth's interest:

Look like th' innocent flower,
But be the serpent under 't (1.6.76–77).

She wants him to appear to be good and kind but to really be deceptive and dangerous under the pleasant facade. This is valuable advice because it works. Now, Macbeth seems to employ it again. He flatters Banquo, calling him the "chief guest" at dinner (3.1.11). He mentions that he was hoping to get Banquo's "good advice" on something, but it can wait until tomorrow instead (3.1.23). He wishes Banquo's "horses [to be] swift and sure of foot" and reminds him to "fail not our feast" (3.1.41, 31). In other words, he appears to be pleasantly interested about the dinner later and even mentions his desire to speak with Banquo tomorrow. In front of Lennox, Ross, other lords, his wife, and their attendants, Macbeth appears to be the innocent flower, but his soliloquy and conversation with the murderers makes it clear that he is the serpent under it. Expressing interest is a good way to appear to be a friend rather than an enemy.

Macbeth was interested in Banquo’s travel plans because he is planning to kill him and his son Fleance.

Macbeth is worried that Banquo is going to tell someone about the witches’ prophecy, or that Banquo suspects him of murdering Duncan.  He is also worried that Banquo might become king, because the prophecies said his sons would be kings.

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 fear'd. ’Tis much he dares, (Act 3, Scene 1)

Macbeth wants to make sure that he knows where Banquo is, because he is sending three murderers after him and his son.  With Banquo out of the way, and Fleance dead, Macbeth will be able to be “safely” in his throne.

Even though Macbeth and Banquo were good friends, once they meet the witches Banquo begins to worry about Macbeth, and Macbeth begins to want to eliminate the threat that is Banquo.

In Act 3, Scene 1, Macbeth asks Banquo about his plans for the day. It is interesting to note that Macbeth asks his most important questions last in two of their exchanges, making them seem like an afterthought and only polite conversation.

"Is't far you ride?"
"Goes Fleance with you?"

People often wait to bring up whatever is really on their minds. For instance, a telemarketer will ask your name and then ask, "How are you today?" As if he cared! And finally he will get around to asking for your donation or whatever he is really calling about. Shakespeare understood human nature, and we can learn some important lessons on that subject from him.

Banquo would certainly not want to leave Fleance alone in Macbeth's castle. Macbeth has two men waiting to talk to him about murdering Banquo and his son. He has to kill both of them. He can hardly kill Banquo and blame Fleance for it; he has used that trick already, and Fleance is too young anyway. Macbeth is fishing. Or phishing. He is trying to figure out the best time and place to ambush Banquo and Fleance. Banquo is courteous, as required by Macbeth's new position, but he doesn't trust him at all. Banquo terminates the conversation by saying, "Our time does call upon's." In other words, "I have to go. We'll be late." We all tell white lies like that. In order to get away from Mr. Spencer, Holden Caulfield lies about having to go to the gym to pick up some equipment in The Catcher in the Rye, and then in order to get away from from the too friendly Mr. Antolini, Holden lies about having to pick up his luggage at the train station. Banquo wants to get away and to avoid providing Macbeth with any further information about his travel plans. Banquo would probably prefer not to return at all, but Macbeth has virtually ordered him to return for the coronation banquet.

Tonight we hold a solemn supper, sir,
And I'll request your presence.
Fail not our feast.

Macbeth talks to the two murderers right after Banquo exits. Macbeth has to be able to tell them where to set up their ambush. He can't just get them to agree to kill Banquo and Fleance and leave the rest up to them. When the two murderers are joined by a third one sent by Macbeth, the Second Murderer says:

He needs not our mistrust, since he
delivers
Our offices and what we have to do,
To the direction just.

After Macbeth and Lady Macbeth hasten the prophesy of the three witches that he will be king by slaying Duncan, Banquo wonders to himself if the other prophesies of the "weird sisters" will also be realized. 

As upon thee, Macbeth, their speeches shine—
Why, by the verities on thee made good,
May they not be my oracles as well,
And set me up in hope? But hush, no more. (3.1.7-10)

Our fears in Banquo
Stick deep, and in his royalty of nature
Reigns that which would be fear'd: 'tis much he dares...
Whose being I do fear; and under him
My genius is rebuk'd, as it is said
Marc Antony's was by Caesar" (3.1.49-55)

As part of his growing paranoia, Macbeth is concerned about Banquo's plans because Banquo has also heard the prophesy about Macbeth and may suspect him of regicide. Also, the witches told Banquo that his sons will be kings, and Macbeth wants to prevent this prophesy from being fulfilled by having him followed and killed.

In Act III, Scene 1, Banquo arrives at the palace and speaks to himself about Macbeth. He remarks that the prophesy of the three "weird women" has come true for Macbeth: He is now king. But Banquo also recalls that the witches told him that he would sire many kings, not Macbeth. Just then, Banquo hears Macbeth approaching and he becomes silent.
When Macbeth enters, he greets Banquo and asks him if he is traveling this day. Banquo replies that he is, but he will return in time to dine with the new king. As soon as Banquo departs, Macbeth orders an attendant to bring certain men before him. As he waits, Macbeth speaks to himself, saying to be king means nothing if he is not safe as the king:

                        ... 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 valor
To act in safety. There is none but he
Whose being I do fear, and under him
My genius is rebuked.... (3.1.50-59)