Act I, Scene 3 of Shakespeare's Romeo and Juliet serves two important purposes. First, it introduces the audience to Juliet and the Nurse. We find out that Juliet is very young, only 13, and that she is very close to the Nurse. In fact, the Nurse literally lives up to her name as she talks about weaning the girl using wormwood. The second purpose is to introduce what would later be the major conflict of Juliet marrying Count Paris. 

Lady Capulet initially wants to speak with Juliet alone, but then thinks better of it and asks the Nurse to stay. We get the feeling she is uncomfortable with her daughter and she needs the Nurse's support. The Nurse proceeds to steal the scene as she recalls Juliet's childhood, particularly the time her husband made a bawdy joke at the toddler Juliet's expense.

Lady Capulet's "purpose" is to ask Juliet if she would like to marry Paris. He is an eligible bachelor who is of the same social and economic status as Juliet and would make a good match, at least in Juliet's parent's eyes. The Nurse is also impressed with Paris and she tells Juliet, 

A man, young lady—lady, such a man
As all the world—why, he’s a man of wax.

I’ll look to like, if looking liking move.
But no more deep will I endart mine eye
Than your consent gives strength to make it fly.