It is a saying that refers to performance art (and sometimes to professional work, in general). It is a way of saying no matter how successful you become, you can't stop working hard, you can't lower your standards, you can't "rest on your laurels." The audience for a live performance only cares about what they hear that night. No matter how great you were five years ago, you are "only as good as your last performance."
It's not something you would use in everyday conversation.
I once read an article by a professional photographer that used the expression. He said that if you are professional, you will be constantly experiencing pressure from clients who want you to do things faster or at lower cost by doing slightly shoddy work. He said that you must say to these clients, "I am a professional. I am only as good as my last job. I can't afford to damage my reputation by putting out anything less than my best work."