If you're unburdened, you don't have anything weighing you down. If you leave that heavy backpack at home, you'll be unburdened as you walk to your friend's house.
People can be physically unburdened, like when it's your brother's turn to carry the picnic basket and you feel unburdened. There's also a figurative or emotional way to be unburdened: "It's pretty unusual to be unburdened by debt when you graduate from college." A burden is something heavy that you carry with you. Physical burdens weigh a lot, and emotional ones (like grief, regret, or hardship) are also heavy.