The "O'Neill," named for Colonel Jack O'Neill, was the first Asgard ship designed solely to fight the war with the Replicators. Its hull, made of a new naquadah, trinium, and carbon alloy, made it the most advanced technological creation of the Asgard, and their last great hope. It was deliberately destroyed in a deception to lure the Replicators away from Thor's homeworld, thus scoring a small victory and giving temporary hope to the Asgard. Later Asgard motherships, including the "Daniel Jackson," were built using a modified but similar design.
Episode Reference: Small Victories