Other forms: unboundedly
Things that are free, rather than attached or restrained, are unbound. You prefer your to wear your hair in a tight ponytail to keep it off your face, while your best friend likes her hair unbound.
If you untie your pet goats so they can roam free, they'll be unbound. It's even more common to use this adjective figuratively, to mean "free" or "unconstrained," like little kids who are unbound from conventional ideas of politeness, or students in the summer, unbound from school, who are free to sleep late.