An audition or a tryout was an opportunity to demonstrate one's skills in order to become a member of a team or program.
In 2375, Benjamin Sisko held tryouts for the Niners baseball team at 1300 hours in holosuite four on Deep Space 9. Rom wanted to play in the hopes of getting closer to his son, while Leeta thought she'd make it a family outing. When Quark expressed his doubt that they would make the team, Rom fired back, "At least we're trying out. What about you?". Quark replied that he had no interest in it.
An audition could be live or recorded. Around 2345, Miles O'Brien's father sent a recorded audition of Miles playing the cello to the Aldebaran Music Academy. Although he got in, he was not interested and signed up for Starfleet two days before he was to leave for the music school. (DS9: "Shadowplay")