Delegation
Assigning your voting power or your stake to someone who acts on your behalf, while you keep ownership of the tokens.
There are two distinct uses of the word. In governance, a holder delegates voting weight to a delegate who researches and votes on proposals; the tokens do not move, and the delegation can be revoked at any time. In proof-of-stake, a holder delegates stake to a validator who runs the infrastructure and shares rewards after commission; the tokens remain the holder's, but the bond is exposed to the validator's penalties. Both forms concentrate influence: a handful of delegates or validators can end up controlling a large share of outcomes, which is why delegate platforms publish voting records and validator sets are monitored for concentration.
In practice
Delegate platforms let token holders assign voting weight to a named delegate who publishes a statement and a record of how they voted on past proposals.
The common misunderstanding
Delegating stake to a validator usually does not hand them your tokens, but it does expose your bond to penalties if that validator misbehaves or goes offline.