Roughly 75 percent of the Manhattan housing inventory is comprised of co-ops. Unlike a condo, co-ops are are owned by a corporation. This means, when you buy an apartment that is in a co-op building, you are not actually buying real property (like you would in a condo). You are in fact, buying shares of the corporation. These shares entitle you to a proprietary lease, which relates your relationship to the building close to that of an investor, rather than a condo building, where you are the outright owner of your specific unit. Usually, the larger the apartment, the more shares you will have in the corporation you have bought into.
Now that you know what it is you are buying, we can now look into how a co-op differs from a condo. First off, the approval process for co-op buildings is significantly more intensive than in condominium buildings. Co-op shareholders, unlike condo residents also pay a monthly maintenance fee to cover building expenses and upkeep like heat, hot water, insurance, staff salaries, real estate taxes and the mortgage debt of the building. Assessments on the building can also be incurred on the building and will (sometimes) drastically affect the value of the property you are considering.
The infamous co-op board sets their own standards in terms of the approval process as well as how the building is managed. Seeing that everyone owns shares in the building, the community as a whole is more concerned with who the building does or does not allow into the building. Co-op boards also require an interview (or interviews) to meet you and ask any questions regarding the information you provided. They can approve or deny any applicant as they choose. The co-op buying (and selling) process is tricky one, where a real estate broker will certainly come in handy.