Susan is the Nurse's deceased daughter, who was born on the same day as Juliet. In act one, scene three, Lady Capulet and the Nurse discuss Juliet's age and Lady Capulet mentions that her daughter is not even fourteen years old yet. The Nurse responds by saying that she knows the exact day when Juliet was born, which was on the night of Lammas Eve. The Nurse goes on to mention that Juliet was born on the same day as her daughter, Susan. The Nurse also comments,

"Susan and she—God rest all Christian souls!—Were of an age. Well, Susan is with God. She was too good for me" (Shakespeare, 1.3.20-22).

It is evident that the Nurse's daughter, Susan, has passed away, and one can surmise that she died at a young age. The Nurse proceeds to mention that it has been eleven years since the earthquake and goes on to tell an unflattering, humorous story about Juliet as a baby. The Nurse's intimate knowledge of Juliet emphasizes their close relationship, which is contrasted with Juliet's relationship with her mother.

Susan is mentioned by the Nurse in Act 1, scene 3 during an argument that she is having with Lady Capulet over Juliet's age.  The Nurse says,

     "Even or odd, of all days in the year,
      Come Lammas Eve at night shall she be fourteen.
      Susan and she (God rest all Christian souls!)
      Were of an age. Well, Susan is with God;
      She was too good for me..." (A. 1, s. 3, lines 20-24)

Susan was the Nurse's daughter who was the same age as Juliet and who died as a very young girl (possibly as a baby).  She uses Susan to prove to Lady Capulet that she knows better how old Juliet is than her own mother knows.