Dual given flight time relates to the time you have spent given instruction in a dual control aircraft. It differs from dual received time which relates to the time spent receiving instruction in a dual control aircraft.
Dual given flight time is logged by the instructor in their logbook after an instructed flight. Dual received flight time is logged by the pilot in the other person’s logbook. The CFI must endorse the dual received flight time, or it won’t be a valid log.
Let’s look at a scenario for clarity.
Two private pilots rent a plane together and go up. Pilot A is a certified flight instructor while Pilot B is not.
Pilot B is the PIC because they are manipulating the controls and take responsibility for the plane. Pilot A acts as a CFI giving instruction to their friend.
After the flight, Pilot A records their time as dual given in their logbook. They do not need Pilot B to sign or endorse this.
Pilot B also records his flight time but as dual received flight time. They need Pilot A to sign and endorse the flight time according to FAA rules.
It’s important to remember that you should only record dual given time if you have been giving instruction. If you went flying with a friend and acted as a passenger, that is you didn’t give instruction, you cannot log dual given time.
Similarly, your friend cannot log dual received time if they did not receive instruction from you while in the air or on the ground.