Julia is a young noblewoman from Verona. In the play, she disguises herself as a boy and follows her boyfriend, Proteus, to Milan, where she catches him trying to hook up with another woman.
At the beginning of the play, Julia seems like she's just as fickle as some of the other characters – she can't seem to make up her mind about whether or not she'll allow herself to fall in love, so she asks her serving woman, "But say, Lucetta, now we are alone,/ Wouldst thou then counsel me to fall in love?" (1.2.1). Just a few lines later, she wonders who should be the lucky guy: "Of all the fair resort of gentlemen/ That every day with parle encounter me,/ In thy opinion which is worthiest love?" (1.2.2). OK, Julia is obviously a very popular girl – she's got suitors coming out of the woodwork just to talk with her.
We soon find out that Julia's had her sights set on Proteus all along. Julia slyly asks Lucetta's opinion of Proteus and, when Lucetta suggests the guy's a clown, Julia is furious: "How now! what means this passion at his name?" (1.2.6). Julia's fickle behavior continues throughout the scene, where she works really hard to conceal her true feelings for Proteus (by sending back a love letter, changing her mind, and then proceeding to tear it up to prove that she doesn't care about love) (1.2). Julia's not the only character to behave strangely. Shakespeare's point seems to be that love makes us do strange things, especially when we try to conceal our feelings.
The thing about Julia, however, is that she turns out to be pretty steadfast in her devotion to her boyfriend, Proteus. After Proteus leaves for Milan, she's determined to be with him and risks everything (including potential unwanted encounters with "lascivious men") by traveling to Milan.
Julia is also pretty clever. In order to travel safely, she disguises herself as a boy, "Sebastian." This is pretty gutsy, don't you think? But then Julia doesn't something pretty strange when she arrives in Milan and catches Proteus hitting on Silvia. Instead of revealing her identity, she takes a job as Proteus's pageboy and then proceeds to run a painful errand – delivering a ring to Silvia on behalf of Proteus. Why would she do this? Is she a glutton for punishment? Is she hoping to size up the competition? We're not exactly sure but we do know this – Julia's not the only character to behave this way. In Twelfth Night, Viola falls in love with Duke Orsino after taking a job as his page boy (also named "Sebastian") and then agrees to delivers love letters to another woman, Olivia.
Julia's disguise is important for all sorts of reasons. First, it draws the audience's attention to the fact that we are watching (or reading) a play in which a male actor is playing the role of a woman who is disguised as a boy. (Women actors, as we know, weren't allowed on the Elizabethan stage, so the parts of women were played by men and boys.) Shakespeare has a lot of fun with Julia's "Sebastian" disguise. Check out what Julia says when Silvia asks "Sebastian" to tell her about Julia:
Our youth got me to play the woman's part,
And I was trimm'd in Madam Julia's gown,
Which served me as fit, by all men's judgments,
As if the garment had been made for me:
Therefore I know she is about my height.
And at that time I made her weep agood,
For I did play a lamentable part:
Madam, 'twas Ariadne passioning
For Theseus' perjury and unjust flight;
Which I so lively acted with my tears
That my poor mistress, moved therewithal,
Wept bitterly; and would I might be dead
If I in thought felt not her very sorrow! (4.4.18)
Shakespeare loves this kind of artistic self-reference – he's always letting us know that we're watching a play and he's always reminding us that the world of the stage is not the real world in which we live. At the same time, when "Sebastian" relates the story of how "his" acting role made Julia "weep," we're reminded of the theater's capacity to move us. For Shakespeare, the theater can also be a reflection of the kinds of emotions we experience in the real world.
It's also interesting that "Sebastian" claims to have worn Julia's clothes when "he" played the role of Ariadne in a church play. "Sebastian's" performance of this "woman's part" was so good, "he" says, that it moved Julia to tears. Ariadne is a figure from Greek mythology. She's famous for hanging herself after her boyfriend, Theseus, breaks up with her. (Never a good idea.) Now, we know that "Sebastian" never played the role of Ariadne in a play. This made up story seems to be Julia's way of expressing her sadness over the loss of Proteus without revealing her true identity, which is kind of touching.