The following explanations can provide mere mortals with superhuman abilities: being born on a special day, being the seventh son of a seventh son, being two thirds God and one third man, training from hell, being the chosen ones of prophecy, divine intervention or patronage, being the child of a mighty hero, being exposed to strange energies from another plane of existence, being transported to the D&D world from Earth, being the reincarnation of a legendary figure, drawing a sword from a tree or stone, having harnessed the latent powers of the mind and body, higher point buy, and because the DM says so.
This list is not complete nor exhaustive.