They’re weird! Simple version: If you own a co op you own a share in a building, and you have to follow the rules set up by your neighbors who are trying to maintain the highest value of the building for all shareholders (owners) by not allowing riskier sublettors and conditions that would require more maintenance. Negatives: have to be able to pay more cash down than condos might require and let board see your finances, may take longer to sell.

If you're familiar with HOAs, a co-op is basically an HOA for an apartment building.

Technically you don't own the unit you live in, you buy shares in the co-op which entitle you to live in the unit you live in, but there's not much of a practical difference.

The practical issues come in with respect to how you use the apartment. Co-op rules usually prohibit subletting and require getting approval before doing renovations (and also time restrictions on renovations) and approval to eventually sell your unit down the road.

Generally speaking, they aren't terrible. Unlike HOA horror stories, co-ops usually don't care about superficial stuff like how you decorate your unit. The rules are primarily there to prevent you from negatively affecting the units around you (i.e., you can't hire some fly-by-night plumber to smash a hole in the wall and install a jacuzzi that ends up flooding the unit below you).

But maybe this is stockholm syndrome talking because there's almost no alternative to co-ops in NYC.

Some units are condos where you do actually own the unit. And that generally comes with a higher purchase price, fewer restrictions, but still some use restrictions because, again, you can't do stuff that would damage the units around you.

The last alternative is buying a house but it sounds like that's not a good fit for you given that you're considering studios.

If you buy a co-op, you would actually become a shareholder in a company that owns the building, but that shareholder ownership also gives you a permanent lease of the unit.

Co-ops require board approval for transactions, so a co-op board could just deny your purchase without giving any reason. And that opens a lot of doors for potential discrimination. The application package you submit to the board can be invasive, like resume, copies of your tax returns, letters of recommendations and such (some describe as more invasive than going to a dentist). They may even require an interview... for what's practically the right to rent a unit after paying a huge deposit.

Despite the difficulties, that may still be a financially sound strategy compared to the alternatives. If you don't plan on living there for many years, it's probably not worth it.

While everyone else's explanations are pretty adequate at explaining what a co-op is one thing that everyone left out is the crazy maintenance fees, these tend to go up every year. I've got friends who have paid off their units but their monthly maintenance fees are more than what some people pay in rent. Every co-op board is different but they're also a lot harder to sell should you choose to move out. Some co-op boards can also make your life difficult. YMMV.