Wuuthrad is a ancient battleaxe once wielded by the founder of the Companions, Ysgramor. Its primary effect is causing double damage to elves, namely Altmer, Bosmer, Dunmer and Falmer. Accordingly, the visage of a screaming elf decorates the axe. Though the conditions of its creation are unknown, Ysgramor carried the axe when he and the Five Hundred Companions drove the elves from Skyrim and Solstheim.
At the start of the game, Wuuthrad is in several fragments, all but one within the Companions headquarters Jorrvaskr. During the course of the Companions quest line, the weapon is reforged and is used to gain access to Ysgramor’s tomb.
After finishing the Companions questline, Wuuthrad can be found in the hands of Ysgramor’s statue at the entrance of his tomb (the statue you first placed Wuuthrad on). You can pick it up and use it as you see fit, though it is no longer a quest item and so has a weight. Wuuthrad can not be improved by smithing, though it can be enchanted.