The Hanging Gardens improves the health of your cities and adds an additional population point in them. It increases the odds of its city generating a Great Engineer.
The more cities you have, the bigger the bonus. Team games will have a very large bonus, as the wonder affects a whole team. Civilizations founded around jungles will notice the greatest impact (as this wonder counteracts the poor growth without adding more unhealthiness).
The Hanging Gardens were a distinctive feature of ancient Babylon. They were a great source of pride to the people, and were often described in accounts written by visitors to the city. Possibly built by King Nebuchadnezzar II in 600 BC, the gardens are believed to have been a remarkable feat of engineering: an ascending series of tiered gardens containing all manner of trees, shrubs, and vines. The gardens were said to have looked like a large green mountain constructed of mud bricks, rising from the center of the city.