The main task is, of course, to find and kill all the bosses and gain their exceptional powers through their trophies. The guide to them is so-called Vegvisir's stone. The first is at the spawn circle and leads to Eikthyr. The second, which leads to Elder, is in the Black Forest either in the burial chamber or in the ruins. The third leads to Bonemass and is in the swamps usually in the Sunken Crypts. The fourth is in ruins somewhere in the mountains and leads to Moder. So far the last one is in the plains and leads to Yagluth. Each boss have specific item, which helps yo in the next biome (Eikthyr - material for pickaxe, Elder - swamp key, Bonemas wishbone, Moder - tears). To summon each boss on his altar, specific items available in the respective biome are needed (Eikthyr - deer heads, Elder - ancient seeds, Bonemas - withered bones, Moder - dragon eggs, Yagluth - totems of the Fulings).
You not need to explore whole map, but in each biome make all available crafting tools and upgrade all your gear to the local maximum.
But many people, after completing this task, create a new world with a new character and roam the map and enjoy, build bases, castles, bridges and other structures, try to kill bosses in specific time-limit or without the death etc etc ...