I believe it means that they take out rapiers and attempt to cut each other down? It was quite the bloody play, as I recall.

[Romances in Shakespeare were always a little messy. Chloe walked up and looked curiously at the script. What part was he in? Was he planning to audition? Oh, that would be fun. She would imagine that he would make a dashing, angry little Tybalt pretty easily.]

Who are you auditioning for?