First, we the audience get to witness first-hand how the guilt of murdering Duncan has played on Lady Macbeth's conscience. We see her washing her hands in an attempt to get the blood of her victim off the hands which held the daggers and helped carry out the deed. We hear her speaking of "the Thane of Fife had a wife...where is she now?" and of the guards in Duncan's bedchamber, and of her own statement to her husband, "a little water clears us of the deed. Put on your nightclothes! It must look like we have slept!" She was the one in charge, and now she is riddled with guilt to the point that she can not be in the dark, always carries a candle with her, and sleepwalks all the while chattering away about the crimes she and her husband have committed.
The second reason it is significant is that the nurse and the doctor are witnessing this horrible confession. The nurse responds with, "I would not have such a heart in my bosom for the dignity of the whole body." So, the rumors are put to rest, at least as far as these two are concerned. The truth is known about the crimes and foul play of the Macbeths ascent to the throne.
Other reasons this scene is significant is to carry out two important themes in the play. One of those is that of sleep or lack of. Macbeth "murdered" sleep when he killed Duncan. His wife is now sleepwalking. Another is that of reality vs. illusion--"her eyes are open...but their sense is shut".
You have a great first answer, but here are some interesting facts:
Sleep walking - which is a normal occurance in children and young adolescents - is considered a symptom of hysteria (and therefore mental instability) in adults. See the following reference for further information.
Repetitive handwashing is one expression of many forms of "compulsive behaviour syndrome, "meaning any form of repeated activity over which the person has no control. Shakespeare has given us a clear demonstration of this disorder, showing its relationship to guilt long before the psychological term (and its correlation to guilt feelings) was coined.