It's caravans. And you have to use the trade options to buy food from a region to fill your caravan. Most units will use 1 or 2 units per day when in starving regions, from my experience. It takes a pretty big unit to use 2. Also, they only feed your own unit. So if you want to feed an entire army, everyone in it needs to have their own caravan, and buy their own food.
It would be nice if we could add some option to allow people to share that food with their other army members. A regular warrior could have 2 caravans, total of 200 food. That would feed a 10-noble army in a starving region for 10-20 days.
