What it is when you push the expedition button, is that the goods needed to build another harbor are collected at the harbor where you started the expedition. They will be visible outside the harbor while they're being collected.
Once all the goods have been collected a ship will pick them up and you'll get a message telling you an expedition is ready. You can then click the ship and give it a direction. Once the ship arrives somewhere you can tell it to build a harbor there or sail on
