The Moria Goblins is the term given to goblins that resided in Moria.
Moria Goblins (the Goblins that dwelt in Moria) were similar to other Orcs of the Misty Mountains. After the Balrog killed King Durin VI, Goblin bands began to raid Moria, pillaging it of its gold, jewels, and Mithril. When Sauron started gathering his forces he sent many goblins and cave trolls to Moria, where they multiplied. When the Dwarves, led by Balin, returned to Moria, the Goblins attacked and killed them, though many were slain. More were killed when the Fellowship passed through Moria, and still more when they pursued their quarry to Lothlórien and were killed by Elves there. In battle, these Goblins used swords, bows, and knives. One "huge Goblin-chieftain, almost man-high, clad in black mail from head to foot," carried a great spear (with which he struck Frodo) and a scimitar.
During the War of the Ring forces from Moria assaulted Lothlórien, but they were driven back.
Portrayal in Adaptations
Peter Jackson's The Fellowship of the Ring
In Peter Jackson's movie, Moria Goblins are shown scuttling out of cracks in the ceiling like cockroaches.