At this point in the play, Macbeth has just sent the murderers after Banquo and Fleance. He is preparing for the feast, and Lady Macbeth tells him that he must be "bright and jovial" in his manner when he gets there, pretending that nothing is wrong. Macbeth replies:

And so, I pray, be you. Let your remembrance
Apply to Banquo; present him eminence,
Both with eye and tongue: unsafe the while that we
Must lave our honors in these flattering streams,
And make our faces vizards to our hearts,
Disguising what they are.

Both husband and wife, who now have so much to conceal, must make their faces as impassive as vizards, giving no clue to the secrets of their hearts, but covering their emotions as a vizard does a face. It is notable that, although he has just arranged for Banquo's murder, Macbeth is expecting to see him at the feast, and specifically counsels Lady Macbeth on how to flatter him. This shows that he is fully prepared for the murderers to fail, and he probably thinks that this mental attitude will allow him to remain calm in any eventuality. The idea that he alone will see Banquo at the feast, after hearing of his death, is too extreme to contemplate, and this is why Macbeth so spectacularly fails to make his face a vizard to his heart.

This type of concealment and impassivity is a motif throughout the play. Macbeth, on learning that he is not to be Duncan's heir, decides that he must hide his actions even from himself:

Stars, hide your fires;
Let not light see my black and deep desires:
The eye wink at the hand; yet let that be,
Which the eye fears, when it is done, to see.

As soon as she raises the idea of murdering Duncan, Lady Macbeth worries that her husband's facial expressions will betray their intent:

Your face, my thane, is as a book where men
May read strange matters. To beguile the time,
Look like the time; bear welcome in your eye,
Your hand, your tongue: look like th' innocent flower,
But be the serpent under't.

Macbeth's determination to make his face a vizard, therefore, runs counter to his nature, and is doomed to failure as soon as Banquo's ghost appears.

In Shakespeare's Macbeth, this quote employs imagery. Figuratively speaking, the idea is that Macbeth and Lady Macbeth must make their faces "like" a vizard over their hearts, such as one would wear a mask over his/her face—to conceal their true feelings.

There is some personification here, as well, because a heart cannot wear a mask or visor, nor can it physically be deceitful—only people can practice deceit.

A vizard is an archaic word for "mask" or "visor." (A visor was what a knight would have attached to his helmet, which he would lower before going into battle, to protect his face.) The protection needed here is to hide the Macbeth's true feelings so no one will suspect the evil that lurks beneath the surface.

One of the themes in this story is deceit, which can be expressed in "appearance vs. reality," as well as in the form of an important quotation by the witches at the start of the play:

Fair is foul, and foul is fair.

Hover through the fog and filthy air. (I.i.11-12)

This quotation means that what looks good and honest (like the Macbeths) can really be dark and evil beneath the surface. The witches' predictions seem to sound wonderful; in reality, they are simply lies to trick Macbeth into forfeiting his eternal soul. We see the theme again as King Duncan enters Macbeth's castle grounds; he speaks of how welcoming and safe it seems there...so much so that the birds make their nests in the eaves. The truth is that it conceals the ultimate evil—that this good and well-loved King will trust those he loves, but will never leave the castle alive.) 

In Act III, scene ii, the Macbeths have successfully killed the King, but Banquo was present to hear the witches predictions. He has already told Macbeth that he will support Macbeth as long as he does not have to compromise his ethics: his beliefs in what is right and wrong. (He cannot be bought.) Macbeth knows that he can never trust Banquo, so he plans to have him (and his son Fleance) killed. Of all they have done together, this is the first plan Macbeth (who was such a coward at first) does not share with Lady Macbeth. In fact, from here on, he goes crazy with killing.

Because Lady Macbeth is unaware of Macbeth's plans, she tries to calm him. He tells her to make sure to show Banquo a great deal of attention: smile at him and compliment him with fond words and thoughts (as the Queen). In this way, he notes, Banquo will not suspect anything. But neither does the Queen, for she then tells him to drop it all:

MACBETH:

Let your remembrance apply to Banquo;

Present him eminence, both with eye and tongue:

Unsafe the while, that we

Must lave our honors in these flattering streams,

And make our faces vizards to our hearts,

Disguising what they are. 

LADY MACBETH:

You must leave this. (33-38)

Macbeth worries aloud about Banquo, but his wife tells him that Banquo will not live forever, and to stop worrying. 

In that Macbeth tells his wife to make "vizards to our hearts," (which reflects "fair is foul"...hide bad thoughts with positive behavior), there is a certain irony in that he is going to do the same thing with Lady Macbeth by choosing not to share his thoughts with her— disguising his purpose, just as he tells Lady Macbeth to act to keep Banquo from becoming suspicious.

Macbeth's intent is to keep Banquo off his guard, and keep his wife from knowing his plans.

This scene occurs as Macbeth has just entered after hiring murderers to kill Banquo and his son Fleance.  Lady Macbeth asks her husband why he seems so troubled, but he does not mention hiring the murderers, only references Duncan in his grave.

 Lady Macbeth suggests that Macbeth be "bright and jovial" among his guests at the banquet that night.

To which Macbeth responds in agreement with the line that they must "make our faces vizards to our hearts/Disguising what they are"  By this, Macbeth agrees with his wife that they must put on the appearance of light-hearted happiness at the banquet that night.  The idea of "faces vizards to our hearts" suggests concealing what the heart may feel with an outward happy face, because Shakespeare's use of "vizard" is like a visor, or covering, typically to the face.  Instead of covering the face, Macbeth recommends that their faces should actually cover what their hearts may be feeling, which in this case, is anything but happiness.