A medial plica is a remnant of an embryonic partition in the knee, and runs along the inner aspect of the kneecap.
As the knee bends the 'shelf' of tissue may also give a sudden snap over the rounded ends of the femur bone.
On the left is a photograph taken during arthroscopy with the scope in the suprapatellar portal, and showing a thickened plica becoming nipped between the patella (above) and the femur (below. You can see this illustrated in the drawing on the right.
When a medial plica becomes abnormally thickened, it can be felt with the finger as a string-like object to the inner aspect of the kneecap.