Deathclaws are the spawn of government tests on Jackson's Chameleons mixed in with DNA of other species. They seem to have a minimal matriarchal society, as there is one "group leader" per pack.
Deathclaws, originally thought to be mutated lizards, are mutant enemies in Fallout that are extremely strong and fast and have enormous claws on their hands. Deathclaws encounters are more likely in areas of the Capital Wasteland furthest from settlements with the exception of the desolate town of Old Olney, where it is practically overrun with them. They can also be found in vast numbers in the underground Deathclaw Sanctuary. Once a Deathclaw is killed, its corpse can be looted for a Deathclaw hand, which is needed to make the Deathclaw Gauntlet.
Deathclaws are possibly the strongest enemy in some of the Fallout games (not forgetting Frank Horrigan), in Fallout 3 they are rarely second to trogs or even a powerful Yao Guai.
In Fallout 2 it is revealed that because of extensive testing using the F.E.V virus that Deathclaw intelligence could be drastically raised, causing them to be able to talk and use tools. You could obtain an intelligent Deathclaw companion, but after progressing through the game, he becomes less and less useful because of his inability to use ranged weapons.
It's advised that you don't take on a Deathclaw is close combat, if at all. Powerful, long-range weapons such as sniper rifles, anti-material rifles and gaus rifles are the best solution for these giant pests. Being on/in an elevated position is also suggested as aiming from a level position is dangerous as they are extremely fast.
Fallout: New Vegas introduces several new types of Deathclaws, including Legendary, Blind, and Young/Child variants. These can be easier and much more difficult to deal with.