[2] Amherst is home to Ponemah Bog Wildlife Sanctuary, Hodgman State Forest, the Joe English Reservation and Baboosic Lake.

On January 18, 1760, the settlement was chartered by the governor of New Hampshire Benning Wentworth, who renamed it after General Jeffery Amherst, who served as Commander-in-Chief, North America during the French and Indian War.

He wed Jane Means Appleton, the daughter of a former president of Bowdoin College, in a house on the town green.

[4] Amherst is located in New Hampshire's 2nd congressional district, represented by Democrat Ann McLane Kuster (D-Hopkinton).

The town is located in New Hampshire's 11th State Senate district, represented by Democrat Shannon Chandley (D-Amherst).

Amherst also shares Hillsborough 37, a single-member district, with the neighboring town of Milford, New Hampshire; it is represented by Democrat Megan Murray (D-Amherst).

Baboosic Lake is farther north, along the eastern border of the town and is fed by Joe English Brook.

Amherst's highest point is on Chestnut Hill at the town's northern border, where the elevation reaches 865 feet (264 m) above sea level.

New Hampshire Route 101 crosses the town, leading northeast into Bedford and then to Manchester, and southwest into Milford.

A spur, New Hampshire Route 101A, crosses the southern part of Amherst, connecting Milford to the west with Nashua to the southeast.