The leg curl is an isolation exercise for the hamstrings, the muscles that run on the back of your thighs. The calves are also assisting the motion as secondary muscles.
Strengthening the hamstrings is very important. For most people, the quads are stronger than the hamstrings, resulting in muscular imbalance that might lead to bad stability in the knee joint and a greater risk of injury.
The leg curl can be done from a seated position or while laying down. Both are a similar movement and work the same muscles. The main difference is that the seated version gives you more isolation of the hamstrings, while the laying variation engages your calves more.
The hamstrings have two functions: knee flexion and hip flexion. While free weight exercises like the deadlift are great to work the hamstrings at the hip joint, there is still a need to work the hamstrings' knee flexion function.
Move your legs in a slow and controlled manner. Don't swing them to fast, especially on the way up, don't just drop the tension on the hamstrings, but move the legs slowly back to the starting position. This will keep the pressure on your hamstrings for a longer time, and will help you to avoid using momentum.
Keep the back and the glutes pressed against the back rest throughout the whole set. If your back begins to arch its a sign you might be using too much weight.
Watch the knees. The leg curl might put a lot of stress on your knees, make sure this exercise doesn't cause you knee pain. if so, try to fix your technique or avoid this exercise all together.
You can focus on different parts of the hamstrings by changing your toes position. Turning your toes inward will focus more on the semimembranosus and the semitendinousus, while turning your toes outward will shift the focus to the biceps femoris.