All New England towns were built around a “common” area where originally, everyone was free to graze sheep and goats. Over the years, these green patches have lost the ungulates and gained a great deal of statuary and memorials. Uxbridge Common is so full of marble and big guns and statues, there’s almost no room for people.
In every city, big and small, the commons have a special place. Often they are the only “green” places remaining in the town. Public events are held there. Fairs, Christmas festival events, and every other state and national holiday, though I think the commons look best at Christmas.
In old English villages, town greens served essentially the same function. A lot of those greens disappeared during “modernization” and industrialization, but in older villages, you can still see that green section in the middle of town.