Prestiging

Prestiging is to train your own teams gym up to make it stronger.
A 'prestiger' is a mon used to do it.

If you use an attacking line up that is half the CP of the weakest mon in the gym, you can get 1000 prestige points for the gym...the amount you gain for the gym decreases as you use stronger mons closer to the opponents CP

It means adding prestige to a friendly gym.

When you battle a gym that is controlled by your team, you can increase its prestige more by using mon with lower cp than its inhabitants. I prestiger is a mon that is good at this function.

It's generally referred to as a Pokémon with good typing and movesets against common gym defenders. The best don't have a very high attack stat to keep their CP lower and generally have better defense and/or stamina.

Tangela, Tentacruel, Parasect, Wigglytuff, Electrode, Slowbro, Cloyster, Ninetails among others.

Get a group of those guys in the 1200-1500 CP range with the right movesets and you won't run into many gyms you can't get 4-5 k a pop.