What exactly is meant by

Is this a good or bad thing. I was under the impression, maybe falsely, that "remastered" was good. I recently bought some cd's on ebay which were advertised as "remastered". How can you tell that they are? Several of them were BMG products. I just need to know if I need to make a complaint.
Remastered simply means that a new 'master' was made of the material. Sometimes when this is done the material is manipulated somewhat, such as converting it to digital from analog. Usually it's noted somewhere on the CD or inserts, or on a sticker on the shrink wrap that it has been remastered or it may say something like "produced from the original masters." Being remastered would not necessarily make the CD worth more or sound better in and of itself.
Original recordings are made with many more "tracks" (channels) than the 2 (or 5 or so) that exist in media that is sold to the public. The multitrack masters are mixed down to 2 or more channels. If the original recordings still exist, they can be remixed in different ways to yield a different final result starting with the same old material.

Two interesting remixes that I know about are the sound track for the movie "Sweet Dreams" (life of Patsy Cline) and the DVDA "Emmylou Harris, Producers Cut".

When Patsy made her recordings, she was in an isolation booth, wearing headphones so she could hear the musicians, and the track of her voice, although old, is of excellent quality. This track was remixed with some of the old accompanyment tracks and some newly recorded tracks to yield a final result that is better than the original releases.

Most of the Emmylou Harris recordings are also very old and were never intended to be more than stereo, but with many tracks available, a multichannel remix could be done. By the way, this DVDA includes a video interview with producer Brian Ahern which discusses in fair technical detail how and why the remix was done the way it was ... very interesting
I think sometimes it's just a duplicate of the original. They may have to change a couple of things to make the verbage legal, "remastered". I've run into the same thing. I bought something a while back that sounded exactly like the original. I'm probably wrong about this, but it sure seems like some of these are total BS. So, ignore my venting and listen Eldartford.

The best idea is to research online before buying.

Remastering in and of itself does not necessarily mean improved sound quality. Recent examples are the Loreena McKinnet remasters. To me they lost some of their textural richness and gained IMO some artificial detail in the upper range. I realize that this is purely subjective but I prefer the orginals in this case.
All that being said though, some remasters are dramatic improvements.
Kinda like re-fried beans.
Re-Mastering is what makes some CDs released on one label seem so much better than the same songs on the original label. There are many examples. One such would be two sets of Motown recordings that happened to be given to me at the same time. There is a 4-disc set released my Gordy on Motown and another release from Rhino called 'Soul Spectacular'. The Rhino versions have relegated the Motown CDs to my car stereo. The improvement in quality is amazing. For better mixing, Rhino is always a good label as is Hear (the Starguck Coffee label) and the are also some amazing Japanese and German labels that are well worth looking for. Labels like Chesky do it right the first time.