A passive mixer (matrix or otherwise) just uses resistors + variable resistors to mix signals. That works but there are various issues, the overall sound comes out quieter etc. It's a 'good'/correct way only to mix low impedance signals eg direct from microphones etc. Line level/amplified signals will still more or less work tho. An active mixer has buffers and/or preamps to solve various impedence etc issues that i don't fully understand, and to make it possible to add gain. Before i made mine active i could still make feedback loops but had to use a lot more boost/distortion pedals; delays, phasers etc don't add much or any gain so it wouldn't feed back at all. I tweaked mine to go above unity gain (i forget/never fully understood exactly how much gain i added but i modified the schematic to have a bit more than usual) so it can feed back on it's own, you can even do pure no-input mixing.
Two things which passive mixers can do but active ones can't, which can be useful for our sort of purposes, is a) work backwards, ie act as a splitter rather than a mixer. b) mix modular synth control voltage signals (well, it's possible to build active one which does but normal powered audio mixers won't I don't believe)
Good introduction to how basic mixer circuits work:
http://sound.westhost.com/articles/audio-mixing.htm
