This happens in Act V, Scene 1. The reason that they are observing Lady Macbeth is that she has been walking in her sleep for some time now and the gentlewoman (like Lady Macbeth's lady in waiting) is worried about her.
In this scene, we find out that Lady Macbeth is feeling very guilty about all the murders that her husband has committed. She feels like the blood from those murders in on her hands and will not come out. So this scene is important because it shows us how her emotional state is deteriorating.
In the last scene in which Lady Macbeth appears in person, she has seemingly gone mad with guilt. It is a jarring juxtaposition between her previous state of being--unflinchingly cruel, powerful, ambitious, and ruthless--and her now vulnerable madness. Her emotions have gotten the better of her.
Lady Macbeth's servant, the gentlewoman/lady-in-waiting, convinces the palace doctor to watch Lady Macbeth as she sleepwalks. In her sleep, she makes crazed references to the murder of King Duncan. The gentlewoman does not want to repeat the words she says out loud, because she is afraid she might be charged with treason if she utters what Lady Macbeth is saying. Thus, she urges the doctor to hear the words for himself. As he observes her madness, he tells the gentlewoman that there is nothing he can do for a malady of the mind. He becomes very worried about her health and safety, but thinks that only God can help her. He instructs the gentlewoman to watch Lady Macbeth closely.
This scene shows the ending of Lady Macbeth. The tragedies that have happened will have preyed on everyone involved, especially the cunning and conniving Lady Macbeth. Even though she got angry with Macbeth for showing signs of remorse and weakness, she succumbs to these things in the end.