Final answer:
The structure that surrounds each myofibril in skeletal muscle fibers is the sarcoplasmic reticulum, which stores, releases, and retrieves calcium ions necessary for muscle contraction.
Step-by-step explanation:
The sleeve-like structure that surrounds each myofibril in skeletal muscle fibers is the sarcoplasmic reticulum (SR). This is a specialized form of endoplasmic reticulum that is essential in the process of muscle contraction and relaxation, as it stores, releases, and retrieves calcium ions (Ca++). When a muscle fiber is stimulated, calcium is released from the sarcoplasmic reticulum, which triggers the interaction between myosin and actin filaments leading to muscle contraction.
In context to the question provided, the correct answer is d) Sarcoplasmic reticulum. The diagram shows this process taking place, demonstrating the role of sarcoplasmic reticulum in excitation-contraction coupling within skeletal muscle cells.