[4] It is located at the High Falls on the Souhegan River, whose plentiful water power provided the mill town with the state's first industries, making cotton and woolen goods.

The Columbian Manufacturing Company was established in 1826 to make textiles in both Greenville and neighboring New Ipswich.

[5] The Columbian is long gone, but its fine brick buildings still dominate the village, kept company by Queen Anne style houses on side streets.

[citation needed] The railroad depot, which still stands, was once an important landmark that put the tiny towns of Mason and Greenville "on the map".

According to the United States Census Bureau, the town has a total area of 6.9 square miles (17.8 km2), all of it recorded as land.

Greenville's highest point is Barrett Hill, near the western border of the town, with an elevation of 1,270 feet (390 m) above sea level.

NH 31 runs north-south for the entire length of the town before entering Wilton to the north.

The highway shares a right-of-way with NH Route 123 which intersects it and runs north to Pleasant Street.

NH Route 124 crosses the southwest corner of Greenville but intersects no other highways within the town limits.