In Monster Hunter, it's possible to break a monster's body parts. If you keep attacking a certain body part for a period of time, you are going to either sever or break it, which in return, will give you various advantages later on.
For instance, the majority of the wyverns in Monster Hunter flail their tails trying to hit you. If you manage to slice the tail off, you will gain an advantage since the range of the tail's attack will be greatly reduced. Plus, you will also be able to carve the tail for an additional/bonus reward.
Breaking a body part also increases your chances of getting a reward associated with that part. If you are in need of a horn in order to craft a weapon that pertains to that monster, be sure to break the actual horn during the hunt. If you are unable to, there is a chance that you'll still get the part as a reward, but it will not be as high as the probability of you getting it if you break it.
Some traditional body parts that are breakable are: tails, horns, faces, claws/talons on the front legs, any sort of spikes, and wings. Keep that in mind during your hunts if you wish to either make the hunt a bit easier for yourself, or if you need a specific body part for a weapon or armor upgrade.