It basically uses digital amps to alter the sound of any incoming audio, no matter what it is. If you wanted a telephone-style conversation in the middle of your song, for example (think Pink Floyd's "Young Lust"), you add a telephone filter track and record your lyrics through it.
I didn't see anything about using standard effects like phaser or echo. It might be in there, or it might just be the amp style.
You definitely do not need a MIDI keyboard to have fun with GarageBand, but if you play piano, having one can certainly let you enjoy it even more by letting you play your own bit and recording the song.