When you go ashore, you move from the water to the land, usually in a boat. When you've tired of canoeing, you can paddle back to the edge of the lake and go ashore.
An old rowboat might wash ashore, drifting up on the beach, or you might bring your kayak ashore after paddling from one island to another. You can also talk about being ashore after spending time on a boat or ship: "I'm ashore until Friday, and then I head back out on the cruise ship." The roots are a-, "to" or "toward," and shore, from the Middle Low German schōre, "shore, coast, or headland."