I Saw Three Ships originates in England somewhere in the 1600's. England, at that time, was absolutely fascinated with the sea. Sailors who had been around the world returned to England with their marvelous tales. England was stretching its arms to the Americas, Africa, India, and beyond.
The song expresses happiness and excitement about the coming of the Christ child, much like the excitement of a ship coming in to port. It is this happiness and joy that makes the song so popular.