Rations are the primary food source for Units. When Upkeep is paid, Rations automatically pop near the Unit they are intended to feed at the beginning of the Side's Turn. Rations can be made unnecessary through the use of provisions or produced through harvesting or forage.
Depending on the type of food, eating extra rations would reduce a unit’s upkeep by a substantial amount. A good solid meal in addition to the popped rations generally means cutting the unit's next turn’s upkeep in half, for barbarian and sided units alike. And prepared meals gives more upkeep relief than just eating raw forage or produce. Digdoug 21
Since captured units' upkeep is paid by the captor, their rations pop at the captor's Turn (as that is the captured unit's turn too). However, the food can be lower quality than the unit is used too. The captor can use provisions to mitigate the upkeep just like for its own units.