Other forms: clinched; clinching; clinches
When you clinch something, you confirm it, the way you clinch a deal with your brother to trade chores next week by shaking hands on it.
The verb clinch arose as a variation of clench, and its original meaning was "fix securely (a driven nail) by bending and beating it back." Out of this sense of securing something physically came the figurative meaning of settling or securing an argument, deal, or bargain. You can also use it as a noun to mean "an embrace or close scuffle," like when a boxing referee pulls fighters out of a clinch.