An incredibly pretentious, smug person who believes they are somehow more unique and special than everyone else, and allegedly don't need to prove it to anyone (or so they claim).
They also unironically idolize the character, Patrick Bateman from American Psycho, treating him as the archetypal sigma male, when said character is actually a depraved psychopath, necrophile and serial killer who is not even supposed to be likable in the first place and was created by the author, Bret Easton Ellis, as a negative caricature of shallow, materialistic yuppies from the 80s. And no, almost none of these "Sigma" males have actually read American Psycho, nor seen its film adaptation, hence why they completely miss the point of his character and admire him for all the wrong reasons.