This was one of New York's first public parks, established in 1733 by local landlords so people living in the area would have a place to walk, bowl, and get away from the noise of the city.
Since it's meant as a quiet park, there wouldn't be much more to tell except that a statue of King George III was placed here in 1770, commissioned to celebrate the repeal of the Stamp Act. In 1771, a wrought iron fence was added around the park - possible to keep malcontents from vandalizing the statue.
In 1776, rebels stormed the park, tore down the statue, and hacked it to pieces. The reason for the attack? They'd just heard the Declaration of Independence read publicly for the first time. Most of the statue was later melted down and turned into musket balls for the Continental Army - perhaps the rebel version of destroying the Liberty Tree for firewood.
The Bowling Green still exists in modern day New York and it's home to another statue: the "Charging Bull" of Wall Street stands just outside the fence. Different times, different icons.