The Qo'Tarl is a Klingon ship that primarily has served the Kre'Tal family (Captain K'Taul's family) since the Vorcha class starships have been in use. It has served as the family's flagship with honor and distinction, and helped defeat the D'Braul family when they attempted to take control of the Klingon Empire and declare war on the Federation. In January of 2379, after Captain K'Taul was expelled from Starfleet for his role in violating the Temporal Prime Directive. Despite Starfleet's admonishion of his actions, since it saved the Klingon Empire and the Federation from a deadly war, he was given command of the family flagship, which later became a part of the Sentinel's Battle Group. During the war against the Kiklar, the ship has managed to inflict massive damage to Kiklar ships, despite the fact that Klingons do not have access to Transphasic torpedo technology. When Kiklar droids attempted to invade the ship, the crew managed to fight each and every one off, a feat even many other Klingon ship crews could not manage.
My knowledge of Klingon ships and technology is fairly limited, and what little I know about Klingon politics comes only from TNG. Naming Klingon ships are purely a guessing game for me, so I have no idea if the name even means anything.