Final answer:
The endomysium is a thin connective tissue surrounding each individual muscle fiber within a fascicle, and it works in conjunction with the perimysium and epimysium to support muscle structure and function.
Step-by-step explanation:
A thin covering that is just deep to the fascia of a muscle and surrounds the entire muscle is called the endomysium. This connective tissue layer encases each individual muscle fiber within a fascicle, which is a bundle of muscle fibers. The perimysium is the connective tissue that wraps each of these fascicles. At the highest level, enveloping the entire muscle, is the epimysium.
These three layers of connective tissue provide support and protection to the muscle tissues, allowing for efficient distribution of blood and nutrients as well as conveyance of the forces generated by muscle contraction to the tendons and, ultimately, the bones.