Coop listings having "No Board approval" ?!

It's a sponsor apartment.

As alpine says, it means the apt is for sale by the original sponsor - it is not a resale. Although you won't need board approval to buy, once in you will be required to adhere to the board's bylaws in regards to things like subletting.

It IS possible to negotiate sponsor rights (which would allow you to rent out the apartment to a third party without board approval) but you would not be permitted to reside in the apartment yourself unless you relinquished said sponsor rights.

To explain further: The sponsor is the entity that originally converted the building to a co-op. Sponsors will often put apartments on the market after long-term renters (who were in place prior to conversion) vacate (read: die).