it's a little odd.
Have you perhaps heard the GBA music of Riviera, then listened to the Full Arranged Soundtrack (which was later used for the PSP version)? Perhaps you're familiar with other OSTs that have "full sound" or "grade up" versions, like the Final Fantasy Tactics OST?
Basically, "remastered" is used in somewhat the same sense it is for movies - the music is done over with higher quality samples and synth, sometimes live instrumentation and even remixing. It's basically inbetween an OST and an arrange album - high quality, very faithful arrangements of all the music (with some things like vocal songs, canon-developing drama tracks and real remixes thrown in).
Each Remasterd Tracks album corresponds to a specific Zero game..
Remastered Tracks Rockman Zero - MMZ
Remastered Tracks Rockman Zero: Idea - MMZ 2
Remastered Tracks Rockman Zero: Telos - MMZ 3
Remastered Tracks Rockman Zero: Physis - MMZ 4
The original album, like the music of the original MMZ, is somewhat crude and rough - the series definitely evolves in style and quality after that. Not everybody likes every album, but most people agree that the Remastered Track albums were a good idea. Inti Creates certainly thought so, as they went on to do them for ZX and ZXA (and they did a very similar thing for the Mega Man 9 AST).
The Rockman Zero Game Music Collection -Rockman Zero 1~3- is, as you might imagine, the original music from the first three games, smushed together like the MMBN albums - which means, unfortunately, that nearly all the tracks only play through once.
There unfortunately hasn't been an OST relase for Z4, ZX or ZXA. (ZX and ZXA did get an odd sort of remix album, ZX Gigamix).
Because the albums are quite popular, you can find most of the original and Remastered music up on youtube by searching for track names. For example, here's the original of Scorching Desert from Z1, and here's the remastered version. Some of the tracks in later games get significantly fuller and more interesting remasterings, but I'm sure you can see how that comparison shows the difference.
edit: oh, and here's a track from ZX that shows what happens when they decide to add something new to a song. Here's the original version of "Onslaught", and here's the ZXA Tunes version (ignore the little musical flourish at the beginning). At first they sound pretty close, but at 1:40 the song goes in a new direction that makes it even better.