This speech sets the mood for the horrible events which will follow...namely the murder of Duncan, which leads to the murders and deaths of so many others.
It prepares the audience for what is to come, teaches them about Lady Macbeth's character and what she is capable of, and also informs the audience as to the type of person Macbeth is. We know, for instance, from her speech, that he would not come up with the idea of murdering Duncan on his own and he certainly would not go through with this plan if she were not there to give him "courage".
The speech also sets up the theme of gender roles--Lady Macbeth at the beginning is more of the pants-wearing character by her own character analysis than her husband who is, according to her, "too full of the milk of human kindness" to do anything against his beloved King.
Setting these two up as strong vs. weak at the beginning makes for interesting comparisons later in the play when Lady Macbeth becomes weaker and more human...guilt-ridden and suicidal and when Macbeth begins planning murders without the help of his horrid wife.
Without that speech, the play would be a very different being. It is essential to not only the plot but character development.
A soliloquy is the window to the mind and soul of a character.The character is alone on the stage talking to himself/herself and he/she expresses his/her deepest psychological yearnings to the audience. Lady Macbeth's soliloquy is important for the following reasons:
1. Macbeth's letter to his wife reveals a lot about his character especially his love and trust in his wife:"my dearest partner of greatness." It is because he loves and trusts her that he confides to her what the witches have predicted.
2. It reveals Lady Macbeth's diabolical nature:instead of advising him against believing the witches' prediction that he would become king she decides to incite him to murder Duncan. She knows fully well that her husband could become king of Scotland only by murdering Duncan.
3. It reveals that Macbeth is "too full o' the milk of human kindness" and how she plans to "chastise him with the valour of her tongue" to fulfill their ambitions. This clearly indicates that Lady Macbeth is the dominant partner in their marriage and that although Macbeth is a brave and courageous military commander he can be easily manipulated by his wife. This has led many critics to conjecture whether Lady Macbeth herself is a witch in human form.