The Commonwealth

 is a place in the East Coast, north of Washington, DC, famous for an organization of scientists that operates from their "Institute". Little is known about the Commonwealth or the Institute other than that they possess highly advanced technology and technological skills. The Institute has created true AI and is capable of creating convincing androids.

"The Commonwealth" may very well refer to the Commonwealth of Massachusetts, and "The Institute" would then refer to the Massachusetts Institute of Technology.

Harkness, Dr. Zimmer and Armitage are from the Commonwealth.

Apperances
 is only mentioned in Fallout 3.