To them, evil is not a bad means to a good end or even a bad means to a justifiable end; to them, evil is the means the end, their motivation, and their justification.
The name of the trope comes from a portmanteau of "evil" and the Internet phrase "for the lulz." This may be because Evil Feels Good while Good Is Boring and dumb, but The Evulz is different from It Amused Me in that the Evulz-seeker need not find any pleasure in their evil acts — in some cases they themselves (also) suffer as a consequence of the crapsack world they inflict upon themselves and others.
Some variants of For the Evulz characters, such as the Straw Nihilist and most notably The Joker, compensate for this character flaw through using philosophy; they question and challenge the heroes' concept of justice, order, reason, and the workings of the world, especially when it's a Crapsack World where those who do evil without any reason whatsoever can get away with it.
The Spear Counterpart of the Psycho Lesbian, and the monosexual counterpart to the Depraved Bisexual.
Usually a villainous take on the Camp Gay or, on the other end of the spectrum, a Manly Gay sexual predator whose preferred "quarry" are straight men or young, naive Twinks.
See also Sissy Villain which is closely connected to this trope.
Helga Schneider remembers watching her mother decorate the family Christmas tree with home-baked biscuits shaped into swastikas and Nazi SS insignia before she deserted their Berlin home during the Second World War.
Compare Made of Evil, which is a character which also does evil for the sake of it, but do so because they are actually an Anthropomorphic Personification of evil.