Monster Hunter is a series where you struggle against a monster, finally beat it, and use the knowledge you gained beating it (and other monsters) to kill them all a few more times, get their parts, and make gear that'll help you in the tougher fights to come. It's an action-packed game that requires you to practice and get better, but also rewards you with plenty of gear that boosts your stats. It's a really rewarding game, both when you finally slay something that's been giving you trouble, and when you craft a weapon or armor set that you've been craving.
There are no health bars on monsters, so you have to really observe them to know where they're at in the battle. They'll drool and limp, telling you that they're hungry and low on stamina, or injured and ready to capture. You can break specific parts on their bodies to increase the chances that specific parts will drop, and you can hit them in specific weak points to deal more damage. This is the first game in a very long time that's actually made me care about boss battles - probably because the bosses are the game.
One of the biggest barriers to entry is the animation priority in the combat, and if you were okay with it in the demo, you'll probably have a grand ol' time with it. Monster Hunter's one of those games that everyone should at least try. If everyone tried it for a few hours, there would probably be more fans outside of Japan.