Knee extension is a movement pattern focused on extending the single degree of freedom of the knee joint to produce power. Since the knee is a pin joint, defined as having one free degree of rotation between the femur and tibia, it can only extend or flex. In the case of knee extension, the powerful quadricep muscle complex is used to produce force. As you probably know from seeing the large quadriceps on elite athletes, the four muscles (quad) that make up the knee extensors act to produce a large amount of force for a variety of tasks. Walking, running, and cycling all use significant knee extension force, as does walking up the stairs. Significantly, since the knee is a pin joint, even lateral movements use knee extension to propel individuals to either side. As a result, knee extension is used in all sports, or any event that involves the lower body. This phenomenon is the reason why knee extension is heavily trained (squats, lunges, box jumps) and heavily researched by sports scientists and biomechanists alike.
This visualization is of a skeleton model of the knee extension movement. This model is oriented such that the body is in a neutral position except for the knee extension. You can imagine that in more complex movement patterns like a lateral cut or cycling, the body may have a more complex geometry and configuration. Regardless of the configuration of the body, since the knee joint and knee extension are so simple, it is common for knee extension to produce a high amount of force. This phenomenon explains to ubiquity of knee extension in human movement.