The figure wears a tunic and a sheep-skin mantle, with a fish's head over his own head, and its skin hanging down his back. He carries a bucket in his left hand and a cone in his right hand with which to sprinkle purifying liquid-- this indicates that he is an abkallu or sage. He was one of a pair guarding the inner face of the entrance to the temple of Ninurta.
Some people believe that the god Dagon, who was widely worshipped by the Western Semites and Canaanites, Philistines, and others (including the Assyrians) was a half-fish half-man god, but there is not yet enough evidence to be sure of this hypothesis. However, if indeed some kind of fish god was revered along the Palestinian coast and also by the Assyrians, perhaps this might have made them pay more attention to the words of a prophet that emerged out of the mouth of a great fish, for news of this miraculous event must have travelled along with Jonah to Nineveh.
For more information on the temple and its god, see the here.