A monster you can hatch from an egg in the game and then use in battle.
Kinda the equivalent of a Pokémon (but you can ride all of them outside battle, each have an advantage while riding like jumping, flying etc.) for this game.
See here http://monsterhunter.wikia.com/wiki/MHST:_Monsties
If you already have a 2DS/3DS you can download the demo and play it and you'll get a better idea.
Whats a 'monstie'?