The Ultimate Vault Hunter Mode (UVHM) is a new playthrough mode introduced in the Ultimate Vault Hunter Pack DLC
It is free, regardless of whether or not you buy the DLC, though it is better to have the DLC because otherwise you will not be able to level past 50
You to have to be level 50 to start it and must have beaten TVHM. Its an entirely new play through(3rd playthrough), which means the difficulty will be scaled much higher.