Plain English Meaning
One wing has noticeably more fuel in it than the other, so the aircraft is heavier on one side.
Full Definition
A condition in which the fuel quantity in an aircraft's left and right wing tanks (or other laterally opposed tanks) is significantly unequal, causing one wing to be heavier than the other and producing a lateral weight imbalance about the aircraft's longitudinal axis.
Context Anchor
Seen during preflight fuel checks, fuel-system discussions, and in flight when selecting tanks or watching fuel quantity indications.
Derivation
“Balanced” comes from the idea of a scale with equal weight on both sides. “Unbalanced” means those weights are not even; here, the uneven weight is fuel in the aircraft’s tanks.