Property is something belonging to a person, group, or government. If something belongs to you than you are considered to be its owner. Anything that can be purchased and sold legally is considered to be the property of the person who buys it. People can do much with their property but there are laws and restrictions on some uses of property.
The first thing that often comes to mind when hearing the term is land. A persons land or home is normally the most valuable thing that they own. People spend years saving to buy their first house and often have long term loan agreements that have to be settled. A loan agreement on the purchase of a house or piece of land is called a mortgage.
The idea that people should be able to do as they wish with their stuff is thought to be a basic human right. If I want to sell something I own or not sell it, I should be able to. There are restrictions on this and those normally include not infringing on another person's use of their property. These tend to come into the area of zoning. It is why we can't have a pig farm in the middle of a large city.
International Property Rights
There are many countries and all have their own laws on just how much control an entity or group can have over the things that they own. Before investing in real estate or other international ventures check local laws to avoid unpleasant matters later.
One interesting thing about owning property is the fact that you may sometimes only own the land itself but not the contents under the land. When purchasing property one should ensure that they own not only the land but any and all mineral deposits under it. A person can sell the mineral rights of their land but retain control over the surface.
Property ownership is a simple thing which tends to be complicated as governments and businesses get involved. The idea of "this is mine to do with as I please" is not always as clear cut as it first appears. Find a lawyer, do a little research, and make sure that you will have the rights you assume you will have before investing in any property purchase.