Sorry for the hiatus, kids. I had finals, then a wedding, and then I spent some time in Boston.
Zazen, sorry to break it to you, but that's basically it. To really "get" minimalism, you have to compare early minimalism (early Steve Reich, phillip glass, john adams, etc, etc) and compare it to other stuff going on in "art" music at the time. The 60's-80's were a big time for composers such as Pierre Boulez, Milton Babbit, and several other serialist and ultra-complex composers who started writing music according to algorithms with no reference whatsoever to tonality or a thought of tone centers.
Compare this, however, to something like John Adams' "aeolian harp", where the same pattern repeats endlessly with minor variations. The piece evolves incredibly slowly, which is supposed to give the music an endless, introspective, meandering quality. Ideally, you don't even hear the music develop.
By most definitions, most electronic music could be considered minimalist. It isn't because you don't typically hear techno in an "art music" setting, so nobody wants to label it that way. I do, though.
Modern minimalist music is called so because of a slow evolution, repetition over development, sparse harmonic material (using only the same 2-3 chords over and over), etc, etc. Look at a piece like Terry Riley's "In C". It's a cluster of sound, yes. But (and this is the important part), there are actually only 30 bars of music that just keep getting layered in new and interesting ways. Same thing goes for Phillip Glass - there may be 70 people playing 70 different things, but you'll find that he just keeps recycling ideas and switching them between performers, so there's little/no new material actually being introduced throughout the piece.