A former small town in the Happy (Pioneer) Valley of Western Massachusetts, Enfield, along with several other towns, was flooded in the construction of the Quabbin Reservoir, built in order to provide water to Boston and other parts of Eastern Massachusetts. It was the largest of the four (the others being Dana, Greenwich, and Prescott). Enfield began as Quabbin Parish in the late 1780s and incorporated in 1816 and, with farming and industry, became one of the wealthiest towns in the state. However, the town's fortunes went downhill with the civil war, and it was moderately depressed by the mid-Thirties, when plans for the reservior were announced.
A farewell ball at the Enfield Town Hall in 1937 attracted about three thousand people; buildings were torn down and cemeteries dug up, people relocated, and flooding started in 1939. No more town.
Alternatively, Enfield is a fictional small town in the Boston area of Eastern Massachusetts, where the Enfield Tennis Academy (also fictional) is located. This is where much of the action in David Foster Wallace's Infinite Jest is centered.
In sum, there is no Enfield, MA. But there is an Enfield, Connecticut, an Enfield, Vermont, and an Enfield, New Hampshite.