In Story Mode, property ownership is about generating weekly passive income and securing vehicle storage.
Properties become available for purchase only after you complete the mission "Nervous Ron" as Trevor.
In GTA Online, properties are functional hubs for businesses, heists, and massive vehicle collections.
Unlike Online, you generally buy properties in person. Look for the "For Sale" sign on the map (a house icon with a dollar sign) and walk up to the physical sign on the property to trigger the purchase prompt.