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