At game start you are assigned a house that you first spawn in. You own this house. You are able to purchase other houses and use them as Fast Travel points, as well as sell houses or rent them out for passive income.
To buy/sell houses you must be inside and close to the center of a house that is allowed to be purchased. Not all houses are allowed to be purchased. When in a valid house and near the center the "Real Estate" menu option will be active.
You cannot own zero houses. The game will not allow you to sell your last remaining house.