A housing co-operative is a group of people who collectively own and manage the place where they live.
They operate like a housing association run by the tenants. The co-op members arrange repairs and improvements, decide about rent and who joins or leaves the co-op. When someone joins the co-op, they buy a share in the whole property, which does not imply individual ownership of their particular home, but rather a share in the whole co-operative enterprise. I.e. the right to live in their own abode, to access common areas, and to vote for a board that manages the co-op.
The legal structure for a housing co-op involves registration as an Industrial and Provident Society - this enables the group to advertise and to issue loan stock to the public. Loan stock allows sympathetic individuals and organisations to offer financial support to the co-op without giving them control in the co-op management.