In unmodded(vanilla) Minecraft, the closest thing to a backpack would be a Shulker. It's, basically, a portable chest. You can name it, dye it, and store items inside. And when you break it, the items remain inside the Shulker so you can carry it anywhere you want and place it down to access the items within it. My favorite part is that you can carry multiple shulkers at once.
Here is the Minecraft wiki page for shulkers: https://minecraft.gamepedia.com/Shulker