The Zoo is a building included in the Brave New World expansion, and replaces the Theatre. Otherwise its function is the same.
A Zoo increases the happiness of your empire, but it cannot provide more happiness than there are citizens in the city. The city must possess a Colosseum before the Zoo can be constructed.
The oldest known zoological menagerie (or "zoo") has been excavated at Hierakonpolis and dates to c. 3500 BC; the oldest existing zoo, the Tiergarten Schoenbrunn in Vienna, evolved from the exotic animal collection maintained by the Habsburg dynasty and was opened to the public in 1765 AD.