Foraging is gathering food from the wildlands. It is also an in-game skill; a noble's skill at foraging seems to be the combination of their Food and Lore skills. Naturally, worshippers of Inilla tend to be good foragers.
The game assumes that some members of your clan forage throughout the year, just as farming happens largely without your intervention. However, if your food situation is poor, you can also send out a foraging mission from the Map Screen (keeping in mind that Inilla worshippers are likely to do best). You can also choose to focus the clan's efforts on a foraging venture.
Wilds magic investment at Sacred Time, Inilla's Rootle blessing, and the Sprouting Shrine all improve your foraging.
There is one known illustrated foraging event in Ride Like the Wind, and a number of unillustrated interactive mini-events.