A housing cooperative is a housing arrangement where all owners of the cooperative ("members") cooperatively own the entire building including all space within it. It is similar to a condo association with a few particular differences: In a condo association, occupants own outright the space inside their units -- we all own everything and have a contract to occupy our space. In a condo association, an unit owner is free to sell their unit to someone else for whatever they can get for it -- we all agree to whom buys into the cooperative and how much a new member pays.
Our particular housing cooperative follows a full-equity model.  Everyone living here are long-term residents.
There are plenty of better definitions out there on the Internet. Contact us if you would like to know more about our particular setup.