"Diablo" is, of course, Satan and the ruler of Hell and punisher of sinners. He plays a role in the background and current events of Guacamelee.
Spoiler warning! This article contains plot details
Cast out of Heaven for rebelling against God, Satan built his own kingdom in Hell and punished sinners sent to him--such as Flame Face, whose head was encased in fire for being an arsonist. He also made deals and tempted people.
Such a one was Carlos Calaca, a mexican charro (horseman) who broke his arm the day before a great competition and would have been unable to compete and achieve his lifelong dream of recognition for his skills.
El Diablo appeared to him and offered a deal: Carlos' soul in exchange for a healed arm. Carlos accepted. He won the competition, and in his moment of triumph, he was snatched into Hell and became a skeleton.
And that's where it went bad for the Devil.
Carlos was extremely bitter about being tricked and dragged out of life in his moment of triumph. He sought out the sorceress X'tabay and with her help he sucker-punched the Devil and turned him into a chicken. He then gained rulership of Hell, reanimating mindless legions of undead, and tunneling for the surface of the World of the Dead. He plans to merge the Living and Dead Worlds so he can become god over both, and everyone agrees this is a really bad thing.
The Devil, for his part, escaped and hid in he living world. Juan encounters him when Juan himself has been turned into a chicken, and he teaches Juan how to change back--he says he could do it himself, but he doesn't want to be seen in the living world.
It's possible for Juan to journey to El Infernio and El Diablo will follow him there. If Juan succeeds in breaking the seals on the Devil's office by completing challenges and gaining gold medals, the Devil will stay there and start trying to sort out the paperwork mess and problems caused by Carlos Calaca's misrulership, while still in the form of a chicken.
It's notable that while El Diablo is, of course, completely evil and the Father of Lies and the Angel of the Bottomless Pit and the Great Beast that is called Dragon, he's a preferable choice to Carlos, whose meddling in the order of all things would unmake all that ever was.