Basically the goal is to collect resources, build up a base, tame (and optionally breed for better stats) creatures, fight the bosses and "ascend". The lore is found by reading explorer's notes scattered across the maps. The lore is actually pretty deep.
For the full story, you play through (maps) the island, scorched earth, abberation (amazing map!) and extinction. Genesis maybe part of those too, but I haven't played that yet.
You can play through the optional maps too (the center, ragnarok, valguero, crystal isles, etc.) but they're not canon; just officially supported expansion maps. They're best for setting up dedicated servers with a group of friends.