The process of muscle contraction involves the myosin head forming a cross bridge with actin, bending backward, and consuming ATP for energy. As ATP is used, it transforms into ADP and inorganic phosphate, allowing for a new ATP molecule to bind, which facilitates the myosin head's return to its resting position. This cycle of binding, bending, and detaching is known as the power stroke, effectively pulling the thin filaments inward within the sarcomere.