Tybalt's death is brought about by Romeo's hand (this comes after Tybalt kills Romeo's best friend, Mercutio, and is the reason behind Romeo's act of violence against Tybalt). Tybalt being a cousin of Juliet, a Capulet, perpetrates the feud occurring between the families (the Montagues, Romeo's family, and the Capulets). When Romeo kills Tybalt, not only does he exacerbate the situation between the families, he is also forced into exile to escape conviction for the murder, barring the two young lovers from remaining together. Now, not only can they see no way to bridge the gap, they can't even carry on in secret. This is the climax of the play (Mercutio's death, at least), as everything from this point forward is a downward spiral of destructive behavior.
Since Romeo killed Tybalt he was banished from the town of Verona meaning he can't stay with Juliet anymore .