There's a lot of confusion around the terms "reissued", "remixed" and "remastered" so I thought I'd outline it very simply here. The confusion is understandable because these terms (particularly "digitally remastered") have been used in marketing with very little regard to what they actually mean.
In any modern recording (since the late 1950's), the outputs of several microphones are recorded on separate tracks on a single piece of tape (or hard drive). This is so that the balance between the instruments can be adjusted at a more studied pace rather than during the performance itself. This also enables effects to be applied to different tracks rather than the whole song.
This multi-track tape is then mixed down to two tracks - the left and right channels required for your stereo - adding the effects and eq and getting the best balance of instruments - this two track tape is what we usually refer to as the "master". In the old days this master tape was then sent off to the pressing plant where it was treated further with eq and compression to optimise it for vinyl - the record was supposed to turn out sounding very much like the master tape - for example, to minimize surface noise, the treble is boosted on the record and then cut by the same amount by your stereo, and to save space on the record and prevent the stylus from jumping a set amount of bass is cut, then boosted back by your stereo - the end result sounding quite like the master tape but minimising some of the limitations of the vinyl medium.
Obviously these techniques are not needed any more and it is possible to send a master tape (providing it's digital already) directly off to be duplicated without mastering. It is usual however to get someone else to master it first. The mastering engineer's job is essentially to make sure the CD will sound good on anyone's stereo, to make sure the tracks are all a comparable and suitable volume, set the gaps between songs and generally tidy up and polish anything missed by the producer - after recording and mixing an album it's easy to get fixated with the minute details of the mix, whereas a mastering engineer hears it with a fresh pair of ears.
Now if an album is re-mixed - it has gone back to the mixing stage and had the balance of instruments and effects changed - by definition a new master is needed of this new mix - for example "Help!" and "Rubber Soul" were remixed in 1987 as well as being "remastered".
A reissue is simply what it says - an album that was out of print is simply printed again from the same master - assuming it's in the same format - if it was a vinyl album and has been reissued on CD for the first time then it has also, by definition, been remastered (a digital master had to be created from the analogue master tape). In the early days of CDs it was common for albums to be described as "reissued" rather than "remastered" which has led some people to believe there is a difference - but the conversion from analogue to digital requires a new master - so the album has been "remastered".
However, these days when an album says "remastered" it usually means that the album was already available digitally but a new digital master has been made...confusing isn't it? A particularly convoluted example is the upcoming Beatles' remasters - officially described as "digitally remastered for the first time" - meaning it's the first time the digital masters have been done again! The albums were digitally remastered in 1987 but they must be calling that a "digital mastering" and this is the first "remastering"...
Why do we need new digital masters though? Because digital technology has progressed incredibly far since the first CDs were available in 1982 - although still using 16 bits at 44.1 kHz, we can now fit a lot more information in those bits.
Some artists have graciously given us several remasters of their albums since the early 1980's - unfortunately the Beatles haven't - the albums in the shops today are still the 1987 versions! Frustratingly, some of the songs have been remastered several times but none of the albums have - we've heard enough to see how good they should sound! I can't wait till 09/09/09!
Anyhow, I hope this helps someone, probably I've just further muddied the waters...but I'll go on more about the Beatles remasters shortly!