When you're unencumbered, you're free of baggage: either you literally don't have a lot of stuff to carry, or you're emotionally care-free.
This word has two closely related uses. A person is unencumbered when they're traveling light — they're not struggling to carry 5 suitcases. But if you have no worries or responsibilities, you're also unencumbered — nothing is weighing on your mind. In both senses being unencumbered means you feel light: either literally or emotionally.