Final answer:
The organ described is a muscle, specifically a skeletal muscle, which consists of connective tissues, muscle fibers, and intramuscular fat, and it is capable of contracting to enable movement.
Step-by-step explanation:
The contractile organ made of connective tissue, muscle fibers, and intramuscular fat is a muscle. Muscle tissue is unique in its ability to contract or shorten, which enables movement. Skeletal muscles, in particular, consist of various integrated tissues including connective tissue layers known as mysia. These layers help structure and compartmentalize the muscle fibers within the muscle. One specific layer, called the epimysium, is a dense sheath of irregular connective tissue that wraps the muscle and allows it to contract powerfully while keeping its structural integrity. Tendons, which are formed from the merging of connective tissues, attach muscles to bones, facilitating movement.
Apart from skeletal muscles, there are also smooth and cardiac muscle tissues, each with their specific functions and locations in the body. However, when referring to the composition of connective tissue, muscle fibers, and intramuscular fat, it is the skeletal muscle that best fits the description provided in the question.