Let's get this started. Mostly with the game, Monster Hunter should be self explanatory, a game about hunting and killing of monsters. MHG is a very easy game to start with the Monster Hunter series, since it's the most recent game and does not have such a heavy learning curve as the others. But it should be noted that the release of MHXX, MHG's expansion/successor which will include more in it than MHG had to offer.
If this guide doesn't leave an impression, then this paragraph will (might(not really), the Monster Hunter Games are very entertaining with a long line of games that feature many challenging monsters, my personal favorite was MH3U, even though people didn't like the water fights against monsters, it had the most interesting/entertaining fights i've ever had the chance to experience. Now go forth and Happy Hunting!