My professor says
Nervus troclearis IV somatomotor fibers supply musculus obliquus superior.
and similarly for nervus oculomotorius III
Nervus oculomotorius postganglionic fibers supply musculus ciliaris, m. sphincter pupillae.
I understand the verb "supply" as "stimulate" or "allow signal pass from the tract to the muscle that contracts or flexes". However, fibers must have some other functions too. So the verb supply seems to be a general term for these functions.
How do fibers control the muscle?