It’s a skill, like concentration. It’s used like concentration is, with it being checked when you’re attacked during a performance for a buff or other bard spell you’ve cast that requires focus. The game does do this (like, it checks your performance skill when attacked while concentrating on a spell), but instead of actually showing your character playing continuously while having one of these spells cast, you just pick a song to play as a free action to just add flavor totally optionally. Now, in, say, Neverwinter Nights when you are concentrating on a skill, your character will play their instrument until they fail a check or the spell ends completely automatically.

Also: You can make money playing instruments. There is even an achievement to make so much.