To break it down some,
Z - Performance/Overclocking/Gamer board. Meant for performance work, and for that person that wants to be able to tweak everything.
B - Budget board, for the person who just needs a motherboard, without the extra features that the others might have.
H - Is mainstream, so it'll likely be somewhere between the Z & B boards.
The numbers on the other hand are just the revisions of the chipset involved. So, revisions of the Z series would be Z77, Z87, Z97, and the next one is rumored to be Z107. It should also be noted that a processor that supports say, the 97 chipset will work on Z, B or H based boards, but it may not be able to utilize all available features that the processor can offer. For instance, if you have an unlocked processor, you'll want a Z based board so that you can overclock. Overclocking is a feature you'll likely lose on the non Z boards.
It's a little confusing, but hope this make it clear!