Performance has to do with doing something: a concert or play is a performance, and if you want to talk about how well the actors did, you'd rate their performance.
The main sense of performance is artsy: actors and musicians (and other performers) give performances. You could praise an actor's performance in a movie, but this word extends to other kinds of work and accomplishments as well. If you're failing math, your performance is below par. An athlete can get in trouble for taking performance-enhancing drugs: drugs that make their performance better. Anytime you're talking about how something or someone works — or performs — you're talking about performance.