Ships' main purpose is getting colonies started, and moving the recources from that colony to where it's needed.
Many islands hold great deposits of recources, but you need shipping to mine it.
As for military uses, that map you are playing can be very easily beaten by building a colony ASAP on the coast near the enemy and pusing inwards very quickly.
Catapults are the most powerfull weapon in the game. Every time it hits it kills a soldier in a military building. It can only target military buildings within it's range, and you can't control what it targets.