What they do on the ship is boil the seawater and catch the condensation for the drinking and bathing water. I think it is called distilling the water but I'm not sure on the technical term. It is purer then bottled water. We just bring along a sports bottle that we bought on our first cruise and fill it with water and ice for bringing to the ports otherwise the water from the tap is fine, but I drink tap water at home too.
There are some sports bottles, I think Brita makes one, that have a filter built right in if you have any concerns about the water. I have seen them at Walmart are they aren't too expensive if you are interested in something like that.