Mastering is a separate art from recording or mixing. According to the Wikipedia article, the principle processes of mastering are:
- Editing minor flaws.
- Applying noise reduction to eliminate clicks, dropouts, hum and hiss.
- Adjusting stereo width.
- Adding ambience.
- Equalize audio across tracks for the purpose of optimized frequency distribution.
- Adjust volume.
- Dynamic range compression or expansion.
- Peak limit.
The common thread between these processes is that they can be performed on the complete mixed recording, not just on individual tracks of a recording. Because of this, mastering can be performed at any time on any audio source.
As for the reason why so many works are remastered, the most likely reason is to keep up with new home theater audio formats. If you have a massive 7.2 surround system, it would be a shame if there wasn't a professionally mastered 7.2 format of "Dark Side of the Moon" to utilize that power. Every time new audio encoding formats become widespread (48kHz at 16bits, 92kHz at 24bits, etc.), your favorite audio source will need to be remastered to sound good in that format.
I fully agree with Austin, so won't cover the same ground.
However, there has been a recent development in 'remastering', which is not to literally remaster the best surviving copy of the original mix [of which there will likely be several, compressed &/or EQ'd for different original purposes - for cutting to vinyl, cassette, etc].
Instead, record companies are going back to the original analogue multi-tracks & cleaning up from that point; then re-creating a close approximation of the original mix, but with modern 'sensibilities' & criteria.
The intention of these remakes is not to alienate the original listener, but to encompass newer listeners for whom the original small bandwidth, poorly compressed, scratchy version would not convince them at all, no matter how well it was cleaned up. There is definitely a limit to what you can do from a mono or even stereo original master, compared to what you can achieve by going to the multitracks & starting over.
This can be somewhat contentious, of course, but the idea is that you do the remix/master to the best possible modern standards without doing anything silly like putting gated reverb on a 1972 snare [case in point, the late 80s 'remasters' of Free's Greatest Hits, complete with hideous added digital reverb on the snare.]
I'll see if I can get permission to post some small educational examples & add to this post.
Edit I got permission to post this tiny snippet to Soundcloud - as the track is already known to have 'escaped', unfortunately.
These are not the full-quality finalised versions of either the original or remaster, but are of just sufficient quality to hear the difference.
Remaster (likewise computerized remastering and carefully restored) alludes to improving the nature of the sound or the picture, or both, of already made chronicles, either audiophonic, true to life or videographer.