The muscles that bend (flex) the fingers are called flexor muscles.
These flexor muscles move the fingers through cord-like extensions called tendons, which connect the muscles to bone. The flexor muscles start at the elbow and forearm regions, turn into tendons just past the middle of the forearm, and attach to the bones of the fingers. In the finger, the tendons pass through fibrous rings called pulleys, which guide the tendons and keep them close to the bones, enabling the tendons to move the joints much more effectively.
Deep cuts on the palm side of the wrist, hand, or fingers can injure the flexor tendons and nearby nerves and blood vessels. The injury may appear simple on the outside, but is actually much more complex on the inside. When a tendon is cut, it acts like a rubber band, and its cut ends pull away from each other. A tendon that has not been cut completely through may still allow the fingers to bend, but can cause pain or catching, and may eventually tear all the way through. When tendons are cut completely through, the finger joints cannot bend on their own.