The Pentagon was the headquarters of the US Department of Defense, so named because the complex, as seen from the air, resembled the five-sided geometric shape. It was located just outside of Washington D.C. in Arlington County, Virginia.
Homeworld Command that handled the defense of Earth and its interests also operated here when it was first created by President Henry Hayes. In 2009, several technology developed and acquired by the SGC and Atlantis expedition were also installed at the Pentagon. Some notable technology were the subspace communication, long-range communication device, and defense technology. Though there might be more technology installed, these are the known that had been mention in the series. (SGU: "Air, Part 1", "Air, Part 2")
The Pentagon took significant damage when a Lucian Alliance Tel'tak with a fifty to seventy megaton Naquadria bomb onboard crashlanded into the side of the building. The goal of the strike was to destroy Homeworld Command, and, presumably, the United States capital of Washington D.C.. MSgt. Ronald Greer and Camile Wray were on Earth via the Long-range communication stones, and elected to defuse the bomb, exposing the bodies of Senator Michaels and Dr. Andrew Covel to lethal radiation levels in the process. Michaels and Covel returned to their bodies and disarmed the bomb, presumably dying of radiation poisoning soon afterwards. (SGU: "Alliances")