A pop-up drain stopper connects directly to a rocker arm. You can find this connection at the bottom of the stopper. A rocker arm is a simple mechanical part that moves back and forth on a horizontal plane. When the rocker arm moves toward the drain stopper, it pushes it up, forcing it out of the drain hole. When the rocker arm moves away from the drain stopper, it pulls the stopper along with it. The top lip of the drain stops when it hits the rim of the drain hole as the rocker arm pulls it, creating a watertight seal.
The linkage on a pop-up stopper connects directly to the rocker arm via a spring. While the rocker arm moves back and forth on a lateral plane, the linkage moves up and down on a vertical plane. When the linkage moves down, it compresses the spring, which pushes the rocker arm toward the drain hole. When the linkage moves up, it pulls the spring taut, which causes the rocker arm to pull away from the drain hole.
The trip lever, which sits on a horizontal plane, connects to the top portion of the linkage. The trip lever on a pop-up tub drain is the part of the drain you operate with your hand. When you move a trip lever up, it pulls the linkage up. When you move the trip lever down, it pushes the linkage down. A vertical piece of metal connects directly to the trip lever and the linkage, serving as the connection between the two.
All Together Now
A schematic drawing of a pop-up tub drain stopper system assumes an "L" shape. The horizontal part of the L contains the rocker arm and the bottom of the drain stopper. The vertical part of the L contains the linkage and the trip lever. The point at which the horizontal and vertical elements meet serves as the meeting point between the linkage and rocker arm. When you move the trip lever, you provide the power, or force, that makes the system work.