What actually happens when an album gets remastered?

A lot of times, current pressings or CDs are being made off of 3rd or 4th generation copies of the master with wear occurring along the way. A true remaster is usually accompanied by a remix and will come from the original tapes.

That said, there are some that aren't much more than leveling of the original mix.

The band re-records it without any flaws or errors.

I've heard his Marillion and Yes remasters, and I agree.

When Dave Mustaine remastered the Megadeth catalog, he did a good job on Killing Is My Business but when he did Peace Sells, he also remixed it in such a way that it's aggravating. He pushed his guitar to the front unnecessarily and almost ruined some songs.

I liked what he did, personally. Unlike many new releases, remasters or otherwise, you can still hear the space between the instruments on SW-helmed projects.

In the purest sense ... after you record the record and mix the tracks, mastering is where you hire a high-dollar set of ears who runs your stuff through the most sophisticated of the day and INSANELY expensive equalizers, compressors, limiters, exciters, plate reverb units, etc., to knock it to the next sonic level and make the levels, the eq curves, the low end and high end ideal for current radio and current player technology and current consumers' ears.

I thought mastering in general was BS and smoke and mirrors until the first time my band at the time sent a record to a very reputable mastering house in NOLA some 20 years ago. We sent him the 16-count Crayola box and he sent us back the 64-count box with the built in crayon sharpener, man it knocked what we did from sounding minors to majors. And we "thought" we sent him what was already a great aural package. Man, he showed us.

Remastering "should" be when you take that 20 year old, 30 year old, etc. mastered record and re-run it through the newest, most sophisticated stuff in today's cutting edge mastering houses. Or get a fresh set of high-dollar ears who puts his twist, his signatures on things in regard to levels (this includes redlining), eq curves, low end/boom overall, etc. Nowadays, it can mean do the 180 and run a "new" recording through "old" technology. Re-recording an instrument's tracks with a new player because the old player got fired and sued you over royalties and you want to end his royalty stream. Simply generating a new stream of revenue on old catalog/ "classic" material because sales have become stale. All kinds of things could be called remastering.

Back to the OP, considering what I just typed, re-mastering is very vague by definition and it can very, very, very often be more of a marketing and sales tool as it is the generation of a "new and improved" product.