An oaf is a stupid, boorish, or clumsy man.
There’s an intimate connection between oafs and elves. In ancient legend, elves weren’t the noble creatures portrayed in Tolkien’s stories but powerful and dangerous supernatural beings who were more likely to harm humans than to help them. Their name says so: it comes from an ancient Germanic term for a nightmare, a close relative of the first element of the modern German Albdruck with the same sense. Among other nasty habits, elves were thought to bring humans bad dreams and to steal their children, leaving changelings in their place.
It’s from that belief that oaf first appeared in English, in the seventeenth century. Originally an oaf was an elf’s child, one that had been left in a poor exchange for a stolen human one. In popular superstition, such children were assumed to be ugly or stupid.
The first forms to appear were ouphe and auf, the former turning up several times in Shakespeare’s plays, though he used it to mean an elf or goblin. Auf appears in 1621 in the Anatomy of Melancholy by Robert Burton: “A very monster, an aufe imperfect”.
By the end of the seventeenth century it had settled to the modern spelling and oaf had moved to mean “idiot child” or “halfwit”, then later took on the senses of a large, clumsy man or boy or a rude and boorish man.