I agree with shakespeareguru in that this speech allows the audience to see the conflict which rages in his mind early on. Notice that as the play develops we get very little such introspection--probably because he's on kind of an autopilot of paranoia and murder in order to maintain his throne. Here, though, we understand that there is still something in him which knows the difference between right and wrong. Later, there is no such apparent conflict--everything is right if it keeps him on the throne.
This scene (really a soliloquy) is also significant for the opportunity it gives Macbeth to converse directly with the audience. Macbeth's motives, his conflicts between acting with "evil" or remaining on the path of good, and his guilt about his actions are often unclear in any given moment, especially early in the play. Others -- Lady Macbeth, Banquo, Duncan, Macduff, and Malcolm are often much more certain and precise in taking their stand for or against acts that might be considered "evil."
In this instance, Macbeth is conversing with the audience, sharing his thoughts about what he is preparing to do. Bear in mind that Shakespeare's audience was not separated from the actors by an imaginary "fourth wall" -- each acknowledged the presence of the other throughout a performance. So, this moment Macbeth has alone onstage with the audience gives him the chance to be quite clear with them about his intentions, regardless of regret or guilt that might set in afterwards. One of the conventions of the soliloquy in a Shakespeare play is that the character is using this opportunity to share their true thoughts and feelings, and so it is for Macbeth in Act II, scene ii.
In Macbeth, the dagger scene provides blood imagery, which contributes to blood imagery throughout the play, such as the "bloody man" who reports on the battle in Act 1, the bloody child in Act 4.1, beheadings in Acts 1 and 5, etc. Macbeth is a bloody play, in which power is won by force, and force triumphs, whether it be good or evil.
It is also still another vision, one of many in the play. Imagined or real, Macbeth's vision establishes his guilt, highlights the deed he is about to do, and demonstrates his "living on the edge," if you will. He is unstable, easily manipulated, makes spontaneous decisions that turn out to be disastrous, and reverts to violence as his "default" mechanism.
The dagger scene also highlights Macbeth's own awareness of his ambition. As he says, his vaulting ambition takes precedence over all other thoughts and emotions he feels. He knows the heinous nature of what he is about to do, as his seeing the dagger demonstrates. But he goes ahead with the assassination anyway.
To me, the significance of this scene is that it gives us an early insight into the personality of Macbeth. In this scene, he is exhibiting characteristics that will be important over the rest of the play.
Think about why he sees the dagger. He sees it because he is planning to kill Duncan. So what does that mean? It means that his conscience is already bothering him. He is deeply troubled by the fact that he is planning to kill the king.
We will see this guilty conscience time and again during this play. Just to cite two examples, Macbeth will be unable to pray after he kills Duncan and he will see the ghost of Banquo later on after he has Banquo killed.
Macbeth is very easily wracked with guilt. The dagger scene is one of our first indications of this aspect of Macbeth's character.
In Act II Sc. 1 takes leave of Banquo and Fleance and then dismisses his servant and gets ready to murder Duncan. The soliloquy that follows clearly reveals the troubled state of Macbeth's mind. The soliloquy begins with Macbeth describing the dagger that he sees suspended in the air right in front of his eyes. Immediately he tries to get hold of it but doesn't succeed. It is then that he realizes that the dagger is an expression of his evil thought to murder the king. It is an embodiment of his evil intentions:
Come, let me clutch thee.
I have thee not, and yet I see thee still.
Art thou not, fatal vision, sensible
To feeling as to sight? or art thou but
A dagger of the mind, a false creation,
Proceeding from the heat-oppressed brain?
This scene is important because Shakespeare uses the technique of the soliloquy to reveal to us the wicked and hypocritical nature of Macbeth. Outwardly he behaves as a gracious host to the king but in his heart of hearts he has planned to eliminate him!