Why are Macbeth's first words, "So foul and fair a day I have not seen," important?
When Macbeth says "so foul and fair a day I have not seen", he is referring to the battle that he has recently fought. It is fair because he has won, it is foul because he has lost fellow soldiers in the battle.
This is important because it ties into the whole "fair is foul" and "foul is fair" motif that is seen through out the play. Notice that the witches say "fair is foul and foul is fair" in the first scene of the play. This sets up the whole parodoxical theme of the play in which things that seem fair (like the prophesy that Macbeth will become king) are also foul(ie he will be king, but his children will not be king.)
I agree with the first answer but would add that the words, "so ( foul and fair a day) I have not seen," are as important as the descriptive words. They let us know that the combination of 'foul' and 'fair' is noteworthy, not ordinary. Noteworthy to a degree never before experienced by Macbeth. It is not just an observation. It is an amazement. This lets us know that we are witnessing strange events, and actions occurring in a heightened, otherworldly, dark and unpredictable atmosphere. Shakespeare, through his words, gives us, right at the very start, the tone, texture, and emotional level that we will be spending the next several hours inhabiting with the characters.
Shakespeare was a MASTER of Stagecraft, or, the art of creating, through the use of the ingredients of the theatre, exactly the affect he wanted to create in the experience of the audience.
These words are important since they immediately introduce us to the theme of paradox and equivocation. Macbeth's statement engenders a clear contrast. Two conflicting ideas are expressed in the same sentence, 'foul' is the direct opposite of 'fair'. This is exactly the kinds of situations Macbeth will be confronted with throughout the play.
The evil sisters sisters, though, do not deem the two as contrasting ideas and treat them as equals. Their paradoxical statement, 'Fair is foul, and foul is fair' is an expression of their duplicity. They intentionally set out to deceive the gullible Macbeth and drive him to strive for ambition. In the process, he commits the most heinous of crimes. Ambition is a good thing and therefore fair. Macbeth's 'overriding ambition,' though, is malevolent and thus foul. Macbeth's desire to achieve the golden round turns him into a remorseless killer who spares no one.
It is not only the witches, though, who practice this kind of dastardly deception. Both Macbeth and Lady Macbeth actually encourage one another to be devious. She for example, tells her husband to 'look the innocent flower, but be the serpent underneath'. He, likewise, advises, 'false face must hide what the false heart doth know.' In both instances they urge one another to appear one way but in actual fact be the exact opposite. The appearance is fair, but the real intent is foul. They are remorseless in this and commit murder without batting an eyelid.
Throughout the play Macbeth commits the most heinous deeds which, to him, are fair measures to protect his position, even though he uses foul means to ensure his security. He has the innocent Banquo murdered and has Macduff's entire family slain because he sees the two men as threats to his status.
However, Macbeth soon realises that he had been misled by the witches' seemingly favourable prophesies. He believed, for example that he was invincible for the witches had told him that:
none of woman born shall harm Macbeth
Macbeth shall never vanquish'd be until
Great Birnam wood to high Dunsinane hill
Shall come against him.
Macbeth realizes his folly in both instances. Firstly, he is told by one of his messengers that Birnam Wood seems to be marching towards the castle. This was Malcolm's troops who had each cut a bough off a tree to camouflage their numbers. Secondly, when he is confronted by Macduff and he commands him to surrender since he is protected by a charm, Macduff tells him that he was not naturally born since he had been from his mother's womb, 'untimely ripped.'
It is then that Macbeth realizes that the game is up and that he had been a pawn in the scheming witches' hands. He refuses to surrender and is killed by Macduff. What had been fair to Macbeth had become foul in the most dramatic and tragic manner.