These are preganglionic filaments that begin (have their cell bodies) in the parasympathetic nucleus of the oculomotor nerve (Edinger-Westphal nucleus) and end in the ciliary ganglia (ganglion ciliaris) located in the eye socket right next to the eye globe.
The ciliaries ganglia contains postganglionic parasympathetic neuronal bodies. These send wires into the eyeball. The postganglionic filaments affect the smooth muscle cells in the iris that cause a pupillary contraction (miosis) and the smooth muscle cells (ciliaris muscle) that allow the curvature of the lens of the eye to change (accommodation) which is necessary for sharp vision at different distances.
When the cilaris muscle contracts, the lens increases its curvature and thus its refractive ability, which means that you can see sharply up close. When the ciliris muscle relaxes, the lens will become "flatter", the refractive ability will decrease and the eye will have adjusted for long-range vision.