Aground

The backpack is back-slot equipment that adds to your max carrying capacity. Along with getting an achievement, it should be a priority goal early-game, as it basically doubles your carrying capacity.

To get it, you will need to find, then complete the first quest for the Hunter. You'll need to progress through the first initial tasks, to the point that you meet up with the Miner, are given the pickaxe, and are given the gift of vertical scrolling. Rest in the hut for a scene. You can then head to the right side of the island, where a cliff blocks your way. When you are close enough to the cliff, a short scene should play out with the Hunter shooting several arrows into a boar. He will come down to you, then chat with you a bit. He'll then ask if you will help him out with hunting.

Accept his quest offer, which requires you to craft a bow and to kill 5 boars. Any boars you have already killed prior to meeting the Hunter count towards the five needed. He will also give you a portable workbench, which can be used in your inventory (or placed on/underground) to build things - including the bow.

At this point, you will need coal (at least 15 pieces to unlock the Smelter), wood (at least 4 for the bow, plus fuel use). and 2 iron ore. Wood can be chopped from trees. Iron and coal can be dug up from underground, though iron is less common. You can follow wyrm tunnels to try and quickly find ore. Once you have enough coal, speak to the builder to build a smelter. You will need fuel (wood or coal) to turn 2 pieces of iron ore into a single iron.

When you have one iron and 4 wood, make a bow with the workbench. After killing five boars and with bow in hand, go back to the Hunter and talk to him. He will give you a backpack, unlocking the achievement and providing you with much-needed carrying space.