Why is the letter that Lady Macbeth receives so important to our understanding of two of the main characters in the play?

The letter that Lady Macbeth receives from her husband in Act I, Scene 5 reveals many things about these two prominent characters (Macbeth and Lady Macbeth). The fact that she is reading the letter alone gives the playwright an opportunity to introduce her to the audience without any distraction from another character, such as her husband or King Duncan. She reveals herself as an extremely ambitious and unscrupulous woman who has the power to manipulate her husband through her superior intelligence. They have a very close relationship, but she thinks he is too soft-hearted. It would appear that Macbeth would never have killed Duncan and never have become king if his wife hadn't goaded him into it. As well as characterizing herself by expressing her secret thoughts, Lady Macbeth characterizes her husband in the following lines.

Yet do I fear thy nature;
It is too full o’ the milk of human kindness
To catch the nearest way. Thou wouldst be great;
Art not without ambition, but without
The illness should attend it. What thou wouldst highly,
That wouldst thou holily; wouldst not play false,
And yet wouldst wrongly win. Thou'ldst have, great Glamis,
That which cries, “Thus thou must do, if thou have it;
And that which rather thou dost fear to do
Than wishest should be undone.

Shakespeare very obviously is trying to retain as much sympathy as possible for Macbeth by casting much of the blame for their joint crime on his wife. Macbeth has strong misgivings about going through with the murder of Duncan and only does so at last because his wife will not allow him any peace unless he goes through with the murder. Some critics have even suggested that they had both discussed murdering Duncan before the play ever opens. And that they have simply been waiting for the right opportunity, which arises when Duncan announces that he will be staying overnight at Macbeth's castle because of the fighting in the region. This has never happened before. Duncan makes this clear when he says:

This castle hath a pleasant seat. The air
Nimbly and sweetly recommends itself
Unto our gentle senses.    (I.6)

This is solely to show he has never been there before and to suggest that it is unlikely he will come back again. It's now or never. They have a golden opportunity to assassinate not only Duncan but his two sons on this night only. As Lady Macbeth tells her husband:

Nor time nor place
Did then adhere, and yet you would make both.
They have made themselves, and that their fitness now
Does unmake you.

Lady Macbeth's reading of the letter reveals many important things: the strong relationship between husband and wife, the fact that they have previouslybeen plotting, the fact that Macbeth is too loyal and too kind-hearted to commit treason and murder, the fact that his wife is the dominant figure in their marriage, and it excuses Macbeth to some small extent for going through with the murder. The play is supposed to be the "tragedy" of Macbeth. The audience must feel some degree of sympathy for the hero in order for it to be a tragedy. Lady Macbeth's function, as seen in her response to the letter, is to take some of the blame off her husband. At least we believe he deeply regrets his crime and believe that he never would have committed it without his wife's insistence.