Cooked up by the "mad, bad, and dangerous to know" Lord Byron, a Byronic hero is an antihero of the highest order. He (or she) is typically rebellious, arrogant, anti-social or in exile, and darkly, enticingly romantic. Did we mention Byronic heroes tend to also be kind of hot? Yeah, that too.
The origins of the Byronic hero can be traced to John Milton's Satan in Paradise Lost. For Byron's version, check out his poem Childe Harolde's Pilgrimage. The notoriously swoon-worthy Heathcliff in Emily Bronte's novel Wuthering Heights is also a very famous Byronic hero(ine).