Welcome Bear refers jokingly to the higher level bears that roam the Western Plaguelands. The joke is that new Undead players, not knowing that Western Plaguelands is a much higher level zone than the adjacent Tirisfal Glades where they begin, wander in from the relatively safe Tirisfal Glades and are horribly murdered by — usually — a decaying bear. Hence, the Welcome Bear. One variant is the Welcome Spider, another recurring Plaguelands mob.
A variation on the Welcome Bear for Alliance players can be an Obsidian Elemental while exploring and accidentally wandering into the Burning Steppes from the Redridge Mountains, or even straying across the river into Duskwood from Elwynn Forest.