UHC is Ultra Hardcore. Basically, really difficult PVP Survival without natural regen and one life to live. Think of it as Minecraft PUBG, only Minecraft did it first. Players drop into a survival world and must gather supplies to build weapons and armor as well as get food, potions, and other items to fight against the other players. Last player standing wins. The map has a world border that after a while begins to shrink until all the remaining players are forced into a tight arena area for the final showdown.
Nitro UHC, which is what's on Dogcraft, is Ren's version of this. It has all the same aspects of regular UHC, but it's called Nitro because it removes a lot of the grind for materials out of the game resulting in a much shorter match time. Animals drop cooked meat, ores drop smelted, enemies drop special resources, etc. Games in Nitro last about 30 minutes where a typical UHC can last hours due to the grinding.
There's lots of videos of normal UHC and Nitro on YouTube if you want to check it out for yourself.
Hope that helps explain it.