According to the Merriam-Webster Dictionary, unencumbered means to be free of encumbrance. An encumbrance is something that places impediment or burden on an activity or person.
The root word of unencumbered is encumber, which dates to 14th century Middle English and stems from the Anglo-French use of the word "encumbrer."
One usage of the word encumber is to describe a hindrance that is based on weight or burden, in both the physical and mental/emotional sense. To be unencumbered could mean to be free of weight or burden.
A hindrance of any kind will result in an encumbrance of a situation. To be free of all hindrances would mean to be unencumbered in that situation.
An encumbrance may often be discussed in a financial sense. A financial encumbrance would mean a lien or financial legal claim. To be unencumbered financially, the person would be free of financial burdens, debts or claims.