Delegation in Cardano governance means handing the voting power of your ada to a DRep, who then votes on governance actions on your behalf. It is a separate choice from staking: delegating stake to a pool secures the network and earns rewards, while governance delegation decides who speaks for you in on-chain votes. The two can point at entirely different parties.
Delegation is done once from your wallet and stays in place until you change it. Your ada never leaves your wallet, and you can switch to another DRep at any time. Instead of a specific DRep you can also pick one of the two predefined options: Abstain, which keeps your stake out of the tallies, or No Confidence, which counts your stake in favor of any motion of no confidence.