I imagine that quads are the muscles used most during a jump. I also imagine that the lower back muscles, calves, hamstrings, and buttocks are using during a jump. I also feel that abdominal muscles would be used, not as much as the other mentioned, but the upper body needs to keep balanced during the jump and I guess that the abs would help with that….
Ya, Glow is right. You use the the gastrocnemius (calf) and the soleus (small muscle near the calf) for plantar flexion. Then the rectus femoris (one of the quads) for knee extension. Really the best exercise for any main muscles in the leg are squats. There are a variety of them and they are one of the best leg exercises. Also try doing seated or standing calf raises with weights.