I haven't installed my toilet yet, so I can't tell you how it works first-hand - but here's the basic idea: The toilet gets filled with several gallons of water (maybe 4? don't remember exactly), and that water gets filtered and recirculated. The minimal water consumption was the main attraction for me.
The toilet has a small built-in holding tank for solid waste, which the is separated from liquid waste/water. Thetford doesn't make any specific claims regarding the capacity, but my conversations with people that have used these toilets suggest that it can handle between 20-30 uses between dumping.
As far as dumping goes, it has a standard permanent-type toilet base, but doesn't need another holding tank because it has one built-in. I think a lot of people just plumb these toilets straight to a dump-valve. But I'm going to run the solid waste through a macerator, and then dump that slurry into a composting tank. Actually, there will be two small composting tanks mounted on/in the trailer. We'll alternate between them to give the waste time to compost. The idea is that I'll never have to deal with dumping toxic doo-doo.
Hope this information is helpful. I've done a lot of research on this topic and I'm pretty pumped on the IDEA of these Electra Magic toilets. Hope they live up to my expectations.