The delegation of Hive Power affects the reward pool. When this occurs, the [account vote of the receiver is altered as if it was owned by said account. The ownership of the HP always lies with the one delegating it. This can be thought of as lending it out.
Under Hard Fork 26, the feature of Resource Credit delegation was added. This allows an account to delegate Resource Credit which allows the delegatee to interact with the blockchain while the delegator still retains the voting weight garnered from the Hive Power.