A co-op is a democratic association that owns and controls an enterprise. It can be any sort of business, and just about any kind of business you imagine has been done as a co-op.
There are "consumer cooperatives" that are owned by the people who use the business, i.e. food co-ops that are grocery stores owned by their shoppers, credit unions that are cooperative banks owned by their depositors and borrowers, rural electric co-ops that are electric utilities owned by their customers, housing co-ops that are apartment buildings owned by the people who live in them, co-op restaurants and breweries and many more. In each of these cases, the consumers are called "member-owners" to indicate that they are both the members of the democratic association and the owners of the enterprise. (Watch out for co-ops that call their member-owners "consumers.")
There are also "worker cooperatives" that are owned by the workers of the business (typically called "worker-owners.") What's different about worker co-ops from other forms of employee stock ownership models is that they're governed by the cooperative principles: one worker-owner, one vote. All manner of worker co-ops exist, from bakeries to home nursing care services to architectural firms to janitorial services to taxi companies, and many more. Some unions have even begun starting new worker co-ops that, in addition to a democratically elected board, also have the protections of union membership and grievance processes.
But that's not all!
There are also "purchasing cooperatives" and "shared services cooperatives" where independent businesses might form a cooperative together to achieve economies of scale. Ace Hardware is one such co-op, as is Burger King. The national parent company is a cooperative owned by the local, independent stores (which are in turn typically privately held.) Typically, the co-op provides to its member-owners wholesale goods at scale and prices competitive to big box or other franchises. It may also provide shared services, like advertising, accounting, benefits, and other services that can be outsourced to the parent co-op at a cost savings to member-owners.
There are "producer cooperatives", typically agricultural. Land O' Lakes Butter and Organic Valley are national co-ops owned by their dairy farmers; Ocean Spray and Sunkist are co-ops owned by their fruit growers. These co-ops provide all the same business products and services that their for-profit competitors do; the difference is that they're owned by the farmers instead of shareholders.
Clearly, the co-op model is flexible and has been used to keep ownership where it belongs in all kinds of businesses. One last thing to blow your mind: there are also "hybrid cooperatives" where the ownership might be in two or more classes. For example, the Weaver Street Food Cooperative in Raleigh-Durham, North Carolina, has both a worker-owner and a consumer-owner membership class. The goal of hybrids is blending the best of both worlds: combining the righteousness and value of workers having an important ownership stake and voice in decisions; with the equity- and debt-raising capabilities of consumer co-ops, and hopefully preserving a powerful sense of identity and ownership in both.
Every co-op has a democratically elected board of directors drawn from the membership. Every member-owner can vote for the board and run for election. Every member of the co-op has a single vote -- "one member, one vote" is the core cooperative principle and what sets it fundamentally apart from the investor-owned paradigm of "one dollar, one vote". Each co-op in the US as well as the world also follows the seven universal Cooperative Principles and the ten Cooperative Values.
Together, the US cooperative sector counts 29,000 co-ops, $3 trillion in assets, $650 billion/year in revenue, 2 million employees and at least 130 million member-owners -- over a third of the country. Co-ops are everywhere (map).
Member-owners' rights are protected by the cooperative's bylaws as well as state statutes. Member-owners can attend meetings, review financial data, access the membership list, propose and vote on changes to the bylaws, and call special member meetings. When a cooperative's governance falls into disrepair and member-owners find that the co-op is in the control of self-serving managers and directors, this last tactic becomes the most important. Generally speaking, if 10% of the co-op's membership is in the same place at the same time, there's nothing they can't legally do to save the co-op. They can dismiss the entire board of directors, elect a new slate, change they bylaws -- whatever intervention is necessary to get the ship righted and the co-op back under member-owner democratic control.
Got other questions about co-ops that weren't answered here? Let us know - thank you!
See also: the Democracy At Work Institute, the think-and-do tank of the worker cooperative movement