There's a particular gene that gets mutated sometimes and when it toggles on it triggers a bunch of other changes that are usually pretty unique to the person, like you might get wings or be able to teleport or you might just look funny and that's it. People with actual useful powers can join the X-Men to protect the mutants that don't from humans that hate us and humans from the mutants who are angry about how we get treated or just want power or money or whatever else.