There are many definitions of audio mastering. Most commonly, though, the term mastering is used to refer to the process of taking an audio mix and preparing it for distribution. There are several considerations in this process: unifying the sound of a record, maintaining consistency across an album, and preparing for distribution.
I've had clients ask me why mastering is necessary, stating things like, "my mixdown sounds great … why would I need to master it?" This article is useful in explaining the need and reasons for mastering, as well as giving an interesting historical timeline of the practice.
I feel mastering is as important (and underrated) in the recording and release process as having a good studio monitor set-up. If you intend to stick with 'the music thing' then you will someday look back with deep regret if you allow an unmastered (or improperly mastered) release out into the world, I assure you. It's important to keep in mind that mastering can't fix a bad mixdown, but it will provide a sonic cohesion that will help make sense of your mix, both in context of its own sounds as well as among other professionally regarded releases.
I'm of the school of thought that you should not master your own music, though I do know some people who do this with good results. I believe you can get a much better master from someone who listens to your songs without bias (or who hasn't heard the music a thousand times like you have). You also have an advantage when using a mastering engineer who does this as an area of focus, rather than as a side-job.
It's a huge bonus if you can sit in with your mastering engineer and observe the process. You'll learn much not only about the art of mastering, but also how your music and mixdowns are perceived by a professional. I once was lucky to have a three day mastering session on my music with the renowned Bob Katz who is based here in Orlando. It was like audio bootcamp … illuminating. The experience definitely shaped the way I think about sound.