Can you explain how Tybalt's character and his actions are key events that help the plot of "Romeo and Juliet" along?

Tybalt's death also provides an opportunity for Shakespeare to show Juliet's unique sense of feminine strength.

Juliet’s reaction to Tybalt’s death suggests that Juliet is stronger than even Romeo.  While Romeo turns to Friar Lawrence for a sense of direction following Tybalt’s death, Juliet relies on herself alone.  She is able to reason herself out of grief as shown when she says,

Back, foolish tears, back to your native spring! 

Your tributary drops belong to woe,

 Which you, mistaking, offer up to joy.

My husband lives, that Tybalt would have slain,

And Tybalt’s dead, that would have slain my husband (III.iii.102-107)

Romeo must rely upon Friar Lawrence to provide the same logical perspective to pull Romeo out of his grief following Tybalt’s death.  The Friar says:

                                                Thy tears are womanish, thy wild acts denote

The unreasonable fury of a beast…

I thought thy disposition better tempered.

Hast thou slain Tybalt? Wilt thou slay thyself,

And slay thy lady, that in thy life lives,

By doing damnèd hate upon thyself? (III.iii.111-119)

The parallels between what Friar Lawrence says to Romeo and what Juliet reasons out herself suggest that Juliet is stronger than Romeo in her self-sufficiency and ability to regulate her own emotional state through logic and reflection.  

While Juliet displays many values that are typically associated with masculinity--- verbal wit, reason, and reflection--, Juliet does not neglect her feminine side.  She stays true to the feminine ideal of chastity and upholds feminine decorum.  Unlike Lady Macbeth who tries to find strength by abandoning her femininity, saying “unsex me here, And fill me from the crown to the toe top-full of direst cruelty,” Juliet finds power in her feminine role as daughter and wife (I.v.41-43).