From Hegel's "Philosophy of Right":

"The Eumenides sleep, but crime awakens them, and hence it is the very act of crime itself which vindicates itself. — Now although requital cannot simply be made specifically equal to the crime, the case is otherwise with murder, which is of necessity liable to the death penalty; the reason is that since life is the full compass of a man’s existence, the punishment here cannot simply consist in a ‘value’, for none is great enough, but can consist only in taking away a second life."

Hegel makes it clear that retribution is not merely revenge of a feudal sort, but a type of universalized morality which the criminal's act made possible: the state in some sense acknowledges the rational maxim of the criminal--i.e. "felonies are permissible"--and applies it to the criminal himself.