Yeah, an eagle is pecking a little at his liver – but seriously, his face shows a disproportionate degree of anguish.
Prometheus is in a bind (literally: the painting is “Prometheus bound” by Rubens) because Zeus is pissed that he stole the secret of fire. As punishment, Zeus sends an eagle to eat Prometheus’ liver. But the liver has an incredible capacity for regeneration – so overnight, Prometheus’ liver grows back. So Zeus sends the eagle again, and the liver regenerates again…you get the idea.
While it’s probably pretty uncomfortable to have an eagle pecking at your liver, the reason Prometheus is so incredibly upset is probably because to the ancient Greeks, the liver was considered to be the seat of one’s soul and intelligence. Had the eagle been pecking at Prometheus’ spleen, say, or his kidneys, maybe it wouldn’t be such an insult. Of course, these organs can’t regenerate as prodigiously as the liver can – so although Prometheus would be less offended, he’d also be dead.