The Nurse says this quote in Act I, Scene 3, when Lady Capulet comes to talk to Juliet about how she feels about getting married.  The Nurse goes on and on about how she raised her and she was Juliet's wet nurse.

The previous answer is correct, but I would like to add a bit of analysis to the importance of the quotation.

The audience learns in Scene III of Act One that the Capulets have employed a nurse for Juliet her entire life, beyond her nursing years and plan to retain her well into the foreseeable future, evidenced here as she croons to Juliet: “God mark me to his grace, / Thou wast the prettiest babe that e’er I nurs’d. / And I might live to see thee married once, / I have my wish” (3.1.59-62).

It might come as something of a surprise to learn that wet-nursing was definitely a hot-button issue in both Renaissance England and Italy. We tend to think that wet-nursing in the Renaissance was accepted by everyone, but this is not so. “Mom should do it,” insists Rudolph Bell, “is what all the popular sixteenth century books recommend, even though it seems that no amount of insistence and argument eliminated the widespread practice.”

By having the Capulets in Italy retain a wet-nurse of questionable character, Shakespeare was playing with the idea of the practice in England. Audience members were, for the most part, acutely aware of the debate. One key aspect of the argument centered on the perceived shirking of duty and neglecting of the child due to the selfishness of elite women. It seems that many upper class women were claiming that their “delicate constitutions” would not allow them to breast-feed their own infants.

Citation:
Bell, Rudolph. "How to Do It: Guides to Good Living for Renaissance Italians". Chicago: The University of Chicago Press, 1999

This line was by the Nurse in Act I, scene iii.