I now have all the information needed from Guyton & Hall to write a complete 3-mark reasoning answer. Here it is:

When a large meal is consumed, the stomach and duodenum become distended with food. This distension activates the gastrocolic reflex (from the stomach) and the duodenocolic reflex (from the duodenum). These reflexes are transmitted via the autonomic nervous system - they do not occur (or occur very weakly) if the extrinsic autonomic nerves to the colon are severed. The reflexes trigger mass movements in the colon - a modified, powerful form of peristalsis in which a constrictive ring forms in the transverse colon and a 20 cm or more segment of colon distal to it contracts as a unit, propelling fecal material en masse toward the rectum.

Mass movements typically occur one to three times per day, most commonly during the first hour after eating (especially after breakfast). A series of mass movements persists for 10 to 30 minutes. When these powerful propulsive contractions force a mass of feces into the rectum, the rectal wall becomes distended. This distension activates stretch receptors in the rectal wall, generating afferent signals that initiate the defecation reflex.

The defecation reflex involves two components: (a) an intrinsic reflex mediated by the enteric nervous system within the rectal wall itself, which is relatively weak, and (b) a more powerful parasympathetic defecation reflex involving the sacral segments of the spinal cord (S2-S4). Sensory signals from the rectum travel to the sacral cord and back via the pelvic nerves, greatly intensifying peristaltic contractions throughout the colon and rectum while causing relaxation of the internal anal sphincter. Simultaneously, the person feels the conscious urge to defecate. This coordinated response - triggered proximally by gastric and duodenal distension after a large meal - explains why the urge to defecate is enhanced after eating.

Summary: A large meal distends the stomach and duodenum → gastrocolic/duodenocolic reflexes (via autonomic nerves) → colonic mass movements → feces propelled into rectum → rectal distension → intrinsic + parasympathetic defecation reflexes → enhanced urge to defecate.