A recording is the recorded audio that's stored on a tape or an electronic device. If you make a recording of your history class lecture, you'll be able to listen to it later when you study for the midterm exam (or when you want to nod off to sleep).
The business of making and selling popular songs can be called "the recording industry," and you can also talk about a recording of your favorite jazz album. In addition to audio recordings, there are also video recordings, like the one you take of your little brother's dance recital or soccer game. Recording comes from the verb record, which we can trace back to the Latin recordari, "remember, call to mind, or be mindful of."