The digestive system was the bodily system that served the purpose of breaking food down into its nutritional components.
The Takret Renth noted as for the reason he was preparing food on a cooking plate on a plasma manifold that the members of his species were unable to digest the Human food. (ENT: "The Catwalk")
The gallbladder, a small organ that held bile from the liver until it was needed for digestion, was also part of the digestive system. A diagram of the Human torso depicting the location of the gallbladder was stored in the USS Enterprise's library computer database. This database was accessed by the Talosians in 2254. (TOS: "The Cage")
When Lwaxana Troi was attracted to Odo in 2369, he attempted to lose her interest in that he couldn't eat as he did not have a digestive system. (DS9: "The Forsaken")
The Doctor was going to have a present topic on Hints for Healthful Living about the Bolian digestive system. (VOY: "Investigations")
Both the USS Enterprise and the USS Voyager have been almost eaten inside of the digestive systems of spaceborne species. (TAS: "One of Our Planets Is Missing"; VOY: "Bliss")