NOTE: As of Jan. 2008, all music at the iTunes Store is DRM-free iTunes Plus content, which removes the need to authorize individual songs.
iTunes Authorization - This terms applies to songs, videos, and other content bought from the iTunes store.
Content at the iTunes store is only able to be shared and played on a maximum of 5 computers (due to the iTunes Store's digital rights management). In order to allow the files to play on these computers, you must authorize them.
When you try to play an item bought at the iTunes store on a computer other than the one it was originally purchased on, a window will pop up asking for authorization. When you successfully enter the correct username and password, the file will play.
In this process, Apple keeps track of how many computers are allowed to play a given file, preventing more than 5 from being authorized at a given time.
It is also possible to deauthorize computers.