Smart people, of course!
Well, that's part of it. Mystery readers come in all shapes and sizes, but I've been to lots of conventions where they gather, and they are a dedicated lot. Authors sometimes cringe at the thought of meeting their fans, because they'll be put to the question: why was Character C's motive so weak? How did Character A travel from New York to L.A. so fast? And did you know that your Character B has blue eyes in book one and green eyes in book two? Oops!
So who are mystery readers? They notice details, like the sleuths they like to follow. They like a puzzle, but it had better make sense when all the pieces are in place. They gobble up mystery novels like tent caterpillars on a maple tree. And they love, love, love to talk about what they like and don't like in the genre.
The differences seem to come in the type of sleuth mystery readers like. Some really get into the smart-mouth hero; others like the reluctant sleuths. Some want lots of detail from the mind of the killer; others like him/her to be remote until the end, when motives spill out in a final desperate scene. Some want all the ends tied up: justice served, evil defeated. Others want recognition at the story's end that life just isn't like that.
So who reads mystery? I was correct at the beginning: smart people of many kinds, many types. The only requirement is the desire to pit your mind as a reader against the mind of the author. Let the battle of wits begin!