Flagellants are smelly religious hobos that fight for the Empire against chaos. In the fluff, they are insane murderhobos who have lost everything, and believe the only path to salvation is to brutally torture themselves, massacre their enemies, and preach their message to any who will hear it (read: anyone within a ten-fucking-mile radius of these screaming cunts).
On the tabletop, they are a ludicrously expensive unit that needs to be in numbers of 30+ to even be worth taking, and even then they'll die to anything within a turn or two of combat. Their strength is that they'll take down whatever they're fighting too. For example, say the enemy has a 500pt unit of chaos knights with a fancy chaos lord marching towards your flank; just send in your 300pt unit of flagellants to delete the fuckers. Sure, your flagellants are dead, but so are the enemy, so who cares.
In total Warhammer: War, they are a bullshit cashgrab for the 'Grim and the Grave' DLC that should have just been in the base fucking game (fuck you, CA). However, they are unbreakable, and are henceforth one of the single greatest meatshields in the game. Just send a battle line of the fuckers against the enemy, and then blow up their rear ranks with mortars and wizards. You win, GG, I hope you enjoyed your pay-to-win bullshit.