Final answer:
Cranial nerves like the facial, oculomotor, and vagus nerves carry preganglionic parasympathetic fibers, which innervate terminal ganglia close to or within target organs and affect various bodily functions.
Step-by-step explanation:
The nerve that carries preganglionic parasympathetic fibers includes cranial nerves like the facial nerve (cranial nerve VII), the oculomotor nerve (cranial nerve III), and the vagus nerve (cranial nerve X). These cranial nerves have distinct preganglionic parasympathetic roles, such as controlling pupillary size via the oculomotor nerve, influencing salivary gland secretion and tear production through the facial nerve, and affecting the heart, lungs, and various abdominal organs via the vagus nerve.
These preganglionic fibers travel to terminal or intramural ganglia near or within the target organs, where they synapse, and the subsequent postganglionic fibers then innervate the target effector tissues.