What is a "prestiger"

https://pokemongo.gamepress.gg/gym-combat-mechanics

TL;DR: A "prestiger" is a low-CP Pokemon with good performance as an attacker into a friendly gym.

A prestiger is generally a pokemon that has higher defensive stats than attack stats, because attack counts more than defensive stats in the CP formula.

It's better to use these pokemons to prestige because you need to be at half CP from the defender to gain the maximum prestige per pokemon defeated (1000 prestige).

It's important to pick a prestiger with mediocre attack stats because he will have more stats at a certain CP.

Let's say you want to prestige against a Rhydon with 2700 CP. The prestiger needs do be 1350 CP to gain 1000 points of prestige against this Rhydon. If you got a Exeggutor and a Meganium at this CP range, even tho Eggy is a better pokemon at max level, at the range of 1350 CP he will have less stats than Meganium. He will reach 1350 CP much faster because of his high attack stat, leaving valuable stats behind, making him the weaker option on this scenario.

To get max prestige of 1000, you need to have a team of attackers with the highest CP of the team being 50% or less of the CP of the mons you are attacking.
You get less prestige for the gym the higher the CP of your strongest mon in the team.

get a 3k+ dragonite, for be able to prestige and gain 1000 poins into the friendly gym you need a pokemon with 1500 cp, however having that cp is not only the thing you should look at, because some pokemons can have different cps regarding to the level

if you get a lvl 30 or high level pokemon which has half of the cp of the dragonite, plus has excellent moveset for attack him, example dewdong or lapras, that is a prestiger, a pokemon which in high level can have the good cp range for be effective at training your friendly gym so you gain 1000 points

To add to the above, having a prestiger with super effective STAB moves is key because you effectively increase your attack stat without increasing your CP.

• The highest points you can gain in a single defender is 1K.
• You can gain the 1K if you use a pristeger at least half a CP of the defender. (note: All 6 Attacker must be half CP vs the defender).

Sample:
Defender: Nite 2000
Attacker: Dewgong 1000 ( The other 5 in a line must be 1000 or below ) After you defeat the defender you can gain 1000 Pristege.

I just want to add to the great posts already in this thread by saying this: think of a good prestige Pokémon as one that is "CP-efficient," i.e. A Pokémon with generally low CP at higher levels, but still good enough base stats and movesets to defeat Pokémon typically found in gyms 2800+ CP etc.

Good examples of this would be Wigglytuff and Umbreon.