Cities and towns in the US were once often built around town squares. Many cities have open public areas like this in Europe and South America where people can congregate. Plaza de Mayo in Buenos Aires comes to mind. Cities in the US haven't been designed around a central town square in a long time, but the term has stuck colloquially.
https://en.wikipedia.org/wiki/Plaza_de_Mayo
Below is a link to William Penn's original plan for Philadelphia, where the city would have a five town squares, with one in the center of each of four quadrants, and the largest in the city center. https://www.researchgate.net/profile/Gary-Libecap/publicatio...
https://lauriephillips.com/philadelphias-five-original-squar...
Boston long had a number of town squares, many of which no longer exist, such as Haymarket Square. https://en.wikipedia.org/wiki/Haymarket_Square_(Boston)