To relinquish something means to let it go or give it up, usually after holding onto it for a while. When you relinquish control of the TV remote to your sister, you're giving up your power to choose what everyone watches. When a chess champion relinquishes her title, she's stepping down from a position she worked hard to achieve.

The word carries a sense of releasing something you have a claim to or power over. A king might relinquish his throne. A quarterback might relinquish his starting position to a younger player. A scientist might relinquish her research notes to a colleague who will continue her work. In each case, there's a letting go of something important.

Relinquish is stronger than simply “give” or “hand over.” It suggests you had real control or ownership first. You relinquish your grip on the monkey bars when your arms get tired. A country might relinquish territory after a war. Notice that relinquishing can involve mixed feelings: you might need to do it, or choose to do it, but there's something significant about what you're releasing.