What is HP used for?
HP stands for hit points. It is the amount of health your Pokémon has. Each attack it takes will take away some hit points, and when it reaches 1 or 0 (1 for friendly gyms, 0 for enemy gyms) it will be defeated. So the more hit points your Pokémon has, the more damage it can take in a fight before being defeated.
Well your Pokemon has HP in battle too. The higher it's HP the more hits it can take, both in training and attacking/defending a gym from an opposing team.