I know you can get them from razing villages, or by buying them. But what do you do with them?
Cattle has two main uses. One of which may be more useful than others.
If you purchase some cattle, you can interact with them on the world map. You will be given two options: Butcher or Move the Herd (I don't remember the exact wording, but these are close).
By choosing to butcher the cattle, you will receive meat in your inventory which will provide food for your party until it is consumed, or spoiled. It's not the cheapest way to get food, but it can help if the town has nothing else.
By choosing to move the herd, you can corral them to another city, or to your Marshal's Army, should the Marshal (or Village Elder) ask for cattle. This will increase your reputation with whomever requested the cattle.
One of the quests that you can get from a village is to bring them cattle. In addition to increasing the village's loyalty, I believe this also has an effect on its prosperity. When you have cattle they appear as a separate entity on the map. You drive the herd by moving your party towards it. The cattle will move generally away from your party (this takes some trial and error) until in range of the village, and then disappear. You can also overtake the herd, which will give you the option to stop them or drive them forward.