Your ranch is where you spend most of your time in the games. It's in a different location each time, depending on where the game takes place, but there is always plenty of space for the monster or monsters to run around, exercise, train, and feed. Most of the time there is room for upgrading, too. If you talk to the builders in town, you are usually able to expand the size of your barns or buildings and house larger monsters (or in the later games, more numbers of monsters at once).
The ranch is where many of the in-game events happen, where your monster trains to raise its stats, and where you recieve your mail. The only game in which you live with someone else on their ranch (instead of owning one yourself) is Monster Rancher Advance, when you live with Zest and Aroma on the Plains of Aspia.