Say you create this beautiful wood sculpture and your happy with it but its not quite finished......now its ready to be sanded, stained, lacquered and polished so that all the deep grain, subtle tones and inner glow that wood can have are expressed and the piece of art is experienced at its fullest potential....this is what a mastering engineer does except to music. It is very complexed and subtle, requires great ears,an acoustically treated room with often audiophile speakers, amps and cabling as well as specific types of equalizers and compressors and pristine converters to enable the mastering engineer to "look" inside the music.
Remastering can refer to where the music was produced for vinyl and needs to be prepared for a digital medium and unfortunately can lead to a modern approach of excessive distortion commonly found in current rock & pop music. It can also refer to more of a revisiting of the music. Perhaps Steve Roach's "Structures form Silence " is an example.....the original release and the Projekt remastered release where the music was readdressed for a reason.