What would cause progressively worse knee pain that stems from behind the knee? It is painful to bend and to walk?

Baker's cyst? Several causes of pain behind the knee. I assume no recent trauma--you may have a baker's cyst--basically a collection of joint fluid extruded outside of the joint and formed sack there behind the knee...As it enlarges, it can cause pain and reduces ability to bend the knee. A bit clot in the back can do so as well, but you don't have other symptoms to suggest that. Consult your doc. Good luck.
Many possibilities. Your pain could be as a result of many different things. A thorough history and physical exam and possibly some laboratory and radiology exams are needed to determine the exact cause. Causes of pain may include: soft tissue masses or cysts, trauma (fracture, tendon or ligamentous tear, arthritis), infection, metabolic conditions (gout), musculoskeletal or biomechanical abnormalities.
Baker's cyst. A focal collection of fluid behind the knee, called a popliteal cyst or baker's cyst, is common, particularly in patients with degenerative joint disease of rheumatoid arthritis. When fluid leaks from the cyst it causes pain and inflammation in the adjacent tissues.