Well, the facts of the matter are pretty straightforward. Ahab, the captain of the Pequod, had his leg bitten off by a white whale named Moby Dick, and ever since he has been on a quest for revenge. Of course, things are not so simple. Critics have pointed out that Ahab has much in common with tragic figures from Shakespeare, especially King Lear; similarities have been drawn to Narcissus, or Prometheus, or Satan (from Paradise Lost), or Oedipus. I think, aside from these literary comparisions, the best way to understand Ahab is that he is someone obsessed, not with a whale, but with a particular view of reality.
Ahab's curse is that he believes he understands the secret nature of existence, the bonds of which he is determined to escape. As he puts it in "The Quarterdeck" chapter:
All visible objects, man, are but as pasteboard masks. But in each event—in the living act, the undoubted deed—there, some unknown but still reasoning thing puts forth the mouldings of its features from behind the unreasoning mask. If man will strike, strike through the mask! How can the prisoner reach outside except by thrusting through the wall? To me, the white whale is that wall, shoved near to me. Sometimes I think there's naught beyond. But 'tis enough. He tasks me; he heaps me; I see in him outrageous strength, with an inscrutable malice sinewing it. That inscrutable thing is chiefly what I hate; and be the white whale agent, or be the white whale principal, I will wreak that hate upon him. Talk not to me of blasphemy, man; I'd strike the sun if it insulted me.
Ahab's hatred of "that inscrutable thing" defines him as a character. He has titanic ambition -- he feels he must challenge God. "All visible objects" are false representations of some higher truth -- so in a sense, Ahab sees mortal existence as a lie, a horrible trick played on him by "some unknown but still reasoning thing." His hatred and thirst for vengeance is all consuming. In Chapter 37, he says: “The prophecy was that I should be dismembered; and—Aye! I lost this leg. I now prophesy that I will dismember my dismemberer. Now, then, be the prophet and the fulfiller one. That's more than ye, ye great gods, ever were.” He feels that in killing the whale, he can (figuratively, I guess) become greater than the gods.
It's not that Ahab is without his humanity; he is married, and in Chapter 128 we learn that he has a young son. But Ahab, as a character, is blessed (or cursed) with the gift of insight; his ability to feel anger and vengeance is so developed, so powerful, it overwhelms every other aspect of his personality.