To unchain is to set free by removing restraints. If you want to ride your bike, unchain it from the bike rack. And if you want your dog to fetch, unchain her so she can run.
If a something is secured with chains, you'll need to unchain it to release it. A high-security prisoner will need a guard to unchain her before she can use the telephone, and workers for an animal rescue organization might unchain dogs that have been cruelly chained outdoors in the cold. Another way to unchain something is more figurative: "I always feel unchained from my obligations when school ends in the summer!"