While music sold by the iTunes Store no longer has DRM, and you don’t need to authorize your computers to play this music, other content from the iTunes Store does have DRM. This is the case for movies, TV shows, apps and audiobooks. To be able to use these files on your computer, and to sync them to iOS devices, your computer needs to be authorized.
This is a simple process. If you try and play, say, a video you’ve downloaded from the iTunes Store, iTunes will display a dialog asking you to enter your Apple ID and password. But you can also do this manually: choose Store > Authorize This Computer, then enter your credentials:
You can also authorize your computer to use Audible.com audiobooks, if you download books from that site. Choose Store > Authorize Audible Account.
As for deauthorizing your computer, this is something you should do if you plan to sell or give it away, or even if you send it out for repairs, because changes to its hardware may remove the authorization. Choose Store > Deauthorize This Computer.
If you’ve forgotten to deauthorize a computer that you’ve sold or given away, log into your iTunes Store account and check the Computer Authorizations section.
You can’t deauthorize individual computers, but you can click Deauthorize All to deauthorize all your computers, then reauthorize the ones you still have, following the steps I described above.