Biography
The archetypal High Fantasy villain, often the Big Bad.
He usually lurks in an intimidating fortress in a near-uninhabitable landscape, plotting to Take Over the World (if he doesn't already rule it or has already taken over parts of it), with hordes upon hordes of beastlike warriors (who may be none too bright) at his beck and call.
There are other, more bureaucratic versions of this character that fall under the "Lawful Evil" heading. What separates an Evil Overlord from those is a near-total absence of politics. No senate recognizes his authority, no Pope elected him, he seldom has need for Royal Blood or a line of succession. He may even be immortal and expects to rule forever. He thinks nothing of resorting to terror, mind control, and/or selective breeding to corrupt and control his armies. The dark realm exists solely to conquer his neighbors' domains, and military service is non-negotiable. (Are you good with numbers? Tough titties.) He is, quite simply, a force of evil.
This character is often deployed as a Satanic Archetype and associated with eternal darkness, fire and brimstone, and Ominous Opera Capes. For this and other reasons, they are generally male, because no woman would be a cruel tyrant who screws up her own realm. Unless she's a queen, that is. Appearance-wise, these characters are usually straight expies of Sauron, clad head to toe in imposing, spiked armor of black iron, or wizened necromancers clad in black robes and deathly pallor. Their origins can vary, but they're most commonly a mortal sorcerer, tyrant or sorcerous tyrant turned terrible and inhuman by their arts, a demon or evil deity of some kind, or a living accumulation of the evil of the world.
There are a few, more interesting exceptions: C. S. Lewis's White Witch was draped in white, symbolic of joylessness, decay, and endless winter, and his Lady of the Green Kirtle was green, symbolic of snakes and venom. Some works also portray these characters as beautiful and radiant, in a subversion of both this trope's usual appearance and of the cultural associations of angelic appearances.
Odds are the Overlord probably wants to establish, or already rules, The Empire. In fact, The Emperor often courts aspects of this trope anyway, and a single character is likely to be both. If he isn't officially titled "Emperor" (and sometimes even when he is) he will instead adopt a grandiose title that openly declares exactly which side he's on, most often "Dark Lord" or "Demon King". What, exactly, he plans to do when he rules the world isn't always clear, but it's never anything good — slavery, misery and toil are the best fates waiting for heroes who fail to thwart him.
In battle, the Evil Overlord can be a variety of things, but he is generally the most powerful of his forces. He can be (and is quite often) a physical warrior decked in armor and usually fighting on the frontlines. Some overlords, however, rely more on magical power and may be frail and weak in battle, but world-bendingly powerful when they have time to scheme and prepare. Others just tend to hang behind the action.
A particularly ambitious Overlord often declares himself a god, and starts a Religion of Evil with him as its heart. In cases where an Overlord actually is a god, he is expanding his empire to attain more worshipers. Heroes will have a difficult time dealing with a godly overlord, as he cannot be fully killed, and often must be sealed away for another generation to deal with.
Compare with The Caligula, an Ax-Crazy and highly unstable ruler which sometimes overlaps with the Evil Overlord. The difference is that while they are both villains, the Caligula enjoys royal background (which is possibly the only reason why anyone puts up with them) and is likely to be just a plain terrible and ineffective ruler, whereas the EO doesn't have to be either.
See also: Overlord Jr., Tin Tyrant (often overlaps) Diabolical Mastermind (the real-world equivalent), and Galactic Conqueror/Dimension Lord (this trope In Space!). Namesake for the Evil Overlord List. For the most common interpretation of these characters in Japanese media, see Maou the Demon King.
Not to be confused with the video game Overlord and its sequels, nor the novel series Overlord (although they both feature one of these guys as the protagonist).