When you buy a house or a condominium, you are getting real property. When you buy a co-op apartment you are not actually purchasing the physical apartment. You’re buying shares in the cooperative corporation that owns the building in which the apartment is located. You will own the number of shares allocated to that apartment. Instead of the deed you receive when you buy a house or a condo, with a co-op you get a stock certificate and a proprietary lease. The lease spells out the rights and obligations of the co-op and the shareholder for the use and occupancy of the apartment. The shareholder becomes part owner of the building and has a proprietary lease for a specific apartment.
A more detailed explanation of what a co-op is and the benefits of living in one is available on the website of the National Association of Housing Cooperatives. There are also several books that can teach you practically everything you need to know about how to buy shares in a co-op and how to live and thrive as a co-operator.