Minecraft Raiding servers allow players to raid bases and players. Usually Raiding servers are combined competitive gamemodes like Factions, but it's also not uncommon to see Raiding allowed on Anarchy servers for example.
Raiding servers are...
Raiding servers are about, as you can imagine, raiding. When players are Raiding another team it's sort of like PvP event between two Teams, but when bases are being raided, attackers mostly use TNT, Creepers and special items, to blow up specific bases and loot them.
Raiding server gamemodes?
Raiding is usually part of Factions, Hardcore Factions and Anarchy servers, rarely Vanilla or SemiVanilla servers, but that's up to the server, generally just about any gamemode can add raiding.