Minecraft KitPVP servers are essentially Minecraft PVP server on which players could fight against each other. Some KitPVP servers also have Kits with potions and are sometimes called PotionPVP servers.
How to play KitPVP gamemode?
Most of KitPVP servers will allow you to select specific gamemode or kit, which is given to you when the fight starts. After that there's only one goal on KitPVP server - you have to defeat your opponent.
Group KitPVP servers...
Some KitPVP Minecraft servers went above and beyond, adding many diffrent gamemodes which can include team fight or even Free For All, where you could fight anyone on your arena.
KitPVP servers are considered competitive and will sometimes use score, points and ELO to rank players, you can expect players to be very expiriencted on those KitPVP servers.