A good question. I have been told many meanings. In Hawaiian I believe it means "sea". In German it means "quay". In Japanese I think it means "shell". So it has many meanings associated coincidentally or not with all things oceanic.
However...more research shows a name Kaius stemming from the RomanCaius that evolved into Caesar. From this it could be it had some meaning associated with a King. So Kai could mean King? The word Caius or Kaius is also a Welsh word that derivated from the Roman but means something completely different...field.
If you find out more...let me know. It's a curious name and I have no idea why my parents gave it to me. Perhaps too many drugs in the 60's? Still it's a great conversation piece.