Property is a general legal category for rights of ownership in land, money, tangible objects, intangible objects, etc.
Property rights in common law countries, e.g. the United States, are usually thought of as a bundle of rights. Traditionally, they are: (1) control over use, (2) right to benefits of property (e.g. mining royalities, farm royalties, etc.), and to (3) transfer or sell. Sometimes a fourth is listed, the right to exclude others, e.g. non-owners.
Not every person, or entity, with an interest in a given piece of property may be able to exercise all of those rights. For example, as a lesee of a particular piece of property, you may not sell the property, which is one of the rights in the bundle reserved for the owner. Similarly, while you are a lesee the owner cannot use her right to exclude to keep you from the property. (Or, if she does you can stop paying rent or perhaps sue to regain access.)
Further, property may be held in a number of forms, e.g. joint ownership, community property, sole ownership, lease, etc. These different types of ownership may complicate an owner's ability to exercise her rights unilaterally. For example if two people own a single piece of land as joint tenants, then depending on state law, each may have limited recourse for the actions of the other. For example, one of the owners might sell her interest in the property to a stranger that the other owner does not particularly like.
Types of Property
Most legal systems distinguish between different types of property, especially between land and all other forms of property. They also often distinguish between tangible and intangible property as well.
In common law, property is divided into:
Personal property in turn is divided into tangible property (such as cars, clothing, animals) and intangible or abstract property (stocks, bonds, bank deposits, derivatives, options, futures, patents, copyrights, trademarks, etc.), which includes intellectual property (though some disagree with the use of the term intellectual property).
What can be property?
Not everything can be property; only those things which others can economically be excluded from can be considered property. Thus the air and the water in the sea belong to no one; though once stored in bottles or tanks, they can be considered property.
Traditionally many things existed that did not legally have an owner, such as commons (land belonging to everyone). But over centuries and millennia law in all societies has tended to develop towards reducing the number of things not having clear owners. This enables better protection of scarce resources, due to the tragedy of the commons. But there are many things today which still do not have owners: seawater, the seafloor (though due to the United Nations Convention on the Law of the Sea, some of it can now be considered in some ways property), celestial bodies, land in Antarctica.
The human body is also often not considered something capable of being legally property of anyone.
In many ancient legal systems (e.g. early Roman law), religious sites (e.g. temples) were considered property of the God or Gods they were devoted to. However, religious pluralism makes it more convenient to have religious sites owned by the religious body that runs them.