It's mostly explained in these patch notes and this explanation:
- Ultimate Vault Hunter Mode is unlocked for a character once they have completed the main story missions in True Vault Hunter Mode and reached level 50.
- Unlike other playthroughs, Ultimate Vault Hunter Mode can be replayed multiple times with players able to reset their overall mission progress at any time from the Main Menu.
- No more tutorial missions -- characters in Ultimate Vault Hunter Mode begin in Southern Shelf with the "Cleaning Up the Berg" mission.
- While playing in Ultimate Vault Hunter Mode, enemies and bosses will scale according to the player's current level or, if playing with others, the highest-level player in that party.
-Gameplay changes in UVHM:
- Enemy health generally increased 4x.
- Enemies now have a moderate amount of health regeneration.
- Increased duration of slag damage multiplier effect.
- Upped the damage that slagged enemies take from 2x to 3x.
- Weapon swap speed increased to better facilitate slag use.
- Enemies now more likely to drop ammo.
- Loot Midgets are now "Legendary Loot Midgets" that can drop Legendary and other top-tier gear.
- Powerful new “Ancient” E-Tech relics and rare Pearlscent-grade weapons can be picked up in Ultimate Vault Hunter Mode.
Generally speaking, enemies are harder, have much more health, slag is much more effective, rare drops are increased and certain new E-Tech relics and Pearlescent (cyan colored) equips are avalible only in UVHM. The E-tech relics and Pearlescents are only availible in UVHM for people with the Ultimate Vault Hunter Upgrade pack ($5 DLC, included for free with the Season Pass).
Note that due to the increased difficulty and increased efficacy of Slag, UCHM is particularly suited to co-op play. Just like in "raid" boss fights, a Siren with Res is always useful.
Note also that the first Ultimate Vault Hunter Upgrade Pack increases the level cap by 11, from 50 to 61, and Ultimate Vault Hunter Pack 2 increases the level 61 cap by yet 11 more levels to 72, and includes new content entitled The Raid on Digistruct Peak.