Informal, some would say derisive, name for a ship that has an aggressively multi-species crew.
There is no formal dividing line that says "X number of species required". A Zoo Ship is as much a matter of command style as number of species present. An uptight straitlaced Captain with one of everything can fail to have a zoo.
Zoos thrive on ships that encourage the expression of the crew's multitude of cultures in a positive way. While some would complain that discipline is lax on such ships that has never been the case. Zoo ships are noted for their tight and upbeat esprit de corps and ingenuity in a crisis. The difference being that "what works" is more important than "what is in the book".
For the first time in Starfleet the Far Sector is building such crews by design and finding the kind of Captains that promote that atmosphere. They are noted for producing more well rounded senior officers than any other area of the Federation.