In a Co-op, ownership of the property is vested in a single entity---usually a corporation. The residents of a co-op building own shares in the corporation, rather than owning the property itself. They are tenants with long-term proprietary leases on their units (they do not own title to their units).
I would ask your Realtor to explain in detail the difference between buying a co-op vs. buying a condominium if you are considering a purchase in a co-op. They are not that common around here, but as you've found, they do exist.
Hope that answers your question, and feel free to reach out if you have others or need help.