Well, speaking only from knowledge of the first game on PS2...
It's basically an action game with fairly complex controls and some RPG-like elements. There's no levels or experience, but killing monsters lets you turn their parts into monster-themed weapons and armor with higher stats.
Most of the monsters you hunt are boss-like, giant dragons and the like. The game has its own ecology and the monsters move around the map and will eat and sleep if you leave them alone.
My experience with the first game was that it actually required a lot of skill and could be really intense and challenging, but it felt immensely rewarding when you actually managed to take something down. I specialized in sword-and-shield class weapons, which had low attack power but high mobility, so it would sometimes take me ~40 minutes to kill the stronger ones solo.
The game also has a nice selection of melee (sword, lance, hammer, etc) and ranged (bowguns) weapon types. Each weapon type has a unique control scheme and requires a slightly different strategy, and there's LOTS of different weapons in each class, each with a unique appearance and some with elemental bonuses. Everything if crafted yourself from enemy parts.
MH3 apparently adds underwater combat and torches for caves. Among other things.
Edit: Online is supposed to be free.
I also forgot to mention that MH3 is supposed to be one of the best looking games on the Wii, if that sort of thing matters to you.