Herds are a resource, and the most basic component of your clan's wealth, consisting of cows and goats. The cow is the basic unit of currency in Six Ages, and your herds are listed by a numerical value equal to the number of cows you own. Horses are kept track of separately.
Herds will grow on their own over time, assisted by an investment in herd magic during Sacred Time, as well as Busenari's Calf Blessing and Uryarda's Kid Blessing. Fully-grown cows and goats provide a steady supply of food in the form of milk, and can be butchered in an emergency to provide additional food.
Periodically you will hear that your herds have damaged the pastures over many years of grazing. While this can be partially dealt with using Ventures, the best solution to the problem is to perform the ritual Busenari Finds the Light and ask the goddess to restore your pastures.
While Riders and Rams alike would probably argue that you can never have too many cows, it is possible to have so many that they exhaust your pastures in less than five years--that is, more often than you can perform Busenari Finds the Light without penalty. This seems to happen when you have over 2500 cows.
Because of their value, cows are frequently sacrificed to the gods, offered to other clans as gifts or as payment for favors, or exchanged in trade. Most raids aim at acquiring a rival clan's cows.
Other clans in the Valley have their own herds. In addition to cows, the Rams also keep sheep, hence their name. The Pure Horse Clan keeps no herds of cows or goats at all, preferring to own only horses.