The phrase "to climb down" means to admit defeat, back away from a position or demand, or change one's opinion or stance due to new evidence or circumstances. It is often used in the context of negotiations where two parties are at an impasse and one side eventually concedes their original demands in order to reach a compromise. The phrase originates from the literal act of climbing down from a high position, such as a tree or mountain, indicating that someone has given up on something they once believed in or were determined to achieve.