How is Nurse a better parent to Juliet than her own actual parents?
During the Medieval and Renaissance Periods of Europe, noble families typically did not care for their own children. From infancy, a child would be cared for by a woman whose own child had died or who made a profession of caring for babies. The birth parents were quite distant from their children and served more as administrators for their child's social appearance. A nurse (also called wet-nurse or nanny) would fulfill all parental roles for a child other than actually giving birth and bestowing a name.
It is apparent in Romeo and Juliet that Juliet has a much closer relationship with Nurse than either of her own parents. Consider Act I, Scene III: here Lady Capulet is quite short with Juliet and tells her that she really should hurry up and get married already. Lady Capulet feels it is her duty to ensure Juliet marries well and will be secure financially and socially for the rest of her life. In contrast, Nurse goes on about how she personally had breastfed Juliet, played with her when she was little, and she wishes to see Juliet in a happy marriage.
Later in the play, Juliet confides in Nurse that she has fallen in love with Romeo. Rather than chastising her or forbidding her from seeing Romeo again, Nurse encourages Juliet to pursue this relationship and even helps enable their meeting and marriage. Imagine what might have happened if Juliet had told Lady Capulet she had fallen in love with a Montague! It is clear that Nurse and Lady Capulet have different ideas about what is in Juliet's best interest--her happiness versus her social and financial security.