Rosaline is the gorgeous and aloof woman Romeo crushes on until he meets the love of his life, Juliet. Rosaline has no speaking part, never appears on stage (according to the stage directions), and isn't even listed in the dramatis personae (the cast list). So, why the heck are we talking about Rosaline in our "Character Analysis" when it's quite possible that she doesn't even exist? Well, we may not hear directly from Rosaline (or even see her unless we watch, say, Zeffirelli's 1968 film adaptation of the play), but we do hear a lot about her from one of the play's major characters, Romeo.
According to Romeo, Rosaline is beautiful and completely unavailable – Romeo tells us she's sworn off boys by taking a vow of chastity (1.1.13). In this way, she resembles the unattainable "Laura," a figure in Petrarch's popular 14th-century love poetry who never gives the poet (Petrarch) the time of day.
Rosaline also seems to resemble the "Youth" in Shakespeare's Sonnets. (In Sonnets #1-17, the Poet spends a lot of time trying to convince the Youth, a young man who refuses to marry and have children, that he should get hitched so he can "bless" the world with a bunch of gorgeous kids.) In Sonnet # 4, for example, Shakespeare writes that if the good looking young man dies without having any kids, his "unus'd beauty must be tomb'd with [him]." Compare this with Romeo's complaint about Rosaline's vow of celibacy:
O, she is rich in beauty, only poor,
That when she dies with beauty dies her store. (1.1.12)
Rosaline's aloofness and commitment to remaining "chaste" makes her a pretty good foil for Juliet, who is very responsive to Romeo's passion and makes no apologies for her sexual desire. (Juliet also has an actual speaking role in the play and she happens to be a fully developed character.)
Over the years, directors have made some interesting choices in casting the roles of Rosaline and Juliet to play up the differences between the two women. In Zeffirelli's 1968 film adaptation of Romeo and Juliet, Rosaline is lovely but she's also very stiff and at least a decade older than Romeo. Zeffirelli's Juliet, in contrast, is a young, lively, mischievous beauty who can't keep her hands off of Romeo.