Along with providing a dedicated space for the storage of Arrows or Bolts Quivers also hold special Item Properties such as Weight Reduction. They were introduced to Sosaria with the arrival of the Elves (at the time of the Mondain's Legacy expansion, which is required to use them).
Although they are not sold by NPCs, Tailors are capable of creating the more basic models (assuming they know the correct Recipe, that is). The most simplistic version - the Elven Quiver - requires just a few scraps of leather in order to be sewn together, however the the more extravagant designs draw on Peerless Reagents for added effect.
Surprisingly, quivers did not exist until the Ultima Online: Mondain's Legacy expansion in 2005. Prior to their introduction, archers simply carried ammunition in their backpack. At one point, the UO development team refered to the inclusion of quivers a mistake. At the time, they argued that they made archers too powerful. Archers were subsequently nerfed, but we got to keep quivers.