Co-ops are any place run by its members, for its members. Instead of shareholders, there are stakeholders. For example, a housing co-op is owned run by the people who live there, a food co-op is owned run by people who buy that food and a workplace co-op is owned run by the workers. There's no middleman making money off of people's labours. The people who own and manage the co-op are also the ones who use it.
Co-ops are anti-hieratical and operate more horizontally. Everyone has an equal stake in the co-op and therefore has an equal say about how things are run. Some co-operatives use elected board members to make decisions but smaller co-ops just decide how things are run amongst themselves. There's typically more control and direct involvement in smaller co-ops.