Iapetus was a Titan, so the son of Uranus and Gaia. He was the husband of Clymene, who bore to him the Titans Promotheus, Epimetheus, Atlas and Menoetius. His name apparently derives from laptop 'to assail', 'strike' (see also Iambe), but whether it is of Greek origin or not, it is almost certainly related to the Biblical Japhet (one of the sons of Noah), whose own name is usually explained as meaning 'spacious' (or 'youthful' or 'beautiful').
It has on the other hand been pointed out that if his name is derived from ipto, 'to oppress', then it will have exactly the same meaning ('oppressed') as that of another Biblical character, Job. Perhaps he was intended to represent a man 'born to misery', or to symbolise mankind itself thus.