There are several possible causes of pain behind the knee. A recent injury can cause pain from a ligament tear. Sometimes a small structure in the knee such as a bursa or plica can become inflamed and cause pain.
You may be describing a condition called patellofemoral pain syndrome (PFPS). This occurs when the kneecap is slightly off center as it slides up and down over the joint. This kind of tracking misalignment can cause the cartilage behind the knee to become torn or frayed.
PFPS is often characterized by pain when descending stairs. There may also be pain when trying to bend at the knee in a partial squat. An orthopedic physician or physical therapist can examine you and determine the cause of your symptoms.