it stands for Digital Rights Media.
When you purchase a music file with DRM, the DRM is to try and prevent other people from using the music file if for some reason you decide to share it with someone else who hasnt paid for the music they wouldnt be able to play it.
in itunes case DRM songs can only be used with things like official iPods and can only be played on the 5 computers that the owner authorizes.
By converting the song to MP3 you are removing the DRM restrictions and putting it in a file format that pretty much all devices can read.
iTunes has the option to convert to the same AAC file format but with out the DRM however your non apple MP3 Player probably doesn't read AAC.
In the beginning this was something that all the major record label required and fought for to try and prevent music sharing and illegal downloads. But the record companies are finally starting to understand that this is actually hurting the consumers more than it is helping. They purchase a song in one store with a DRM and then later they buy a new music playing device that doesnt support that type of file DRM. They are starting to allow companies to sell the songs without DRM's.
Amazon sells in normal MP3 format and iTunes now sells in both DRM and in what they call "PLUS" if you buy a song and it has a PLUS next to the price that means that the song wont have DRM protection (however they charge like 20 cents more for the PLUS songs)