E-6 TACAMO refers to several things: a specific aircraft type, the unit that operates it, and a role in the nuclear command and control of the United States. The aircraft, the E-6B Mercury, replaces the functions of two other aircraft: a modified Marine KC-130 tanker that provided provided communications connectivity to U.S. submarines armed with submarine-launched ballistic missiles, and an Air Force EC-135 LOOKING GLASS airborne command post for the Strategic Air Command. Both functions are critical to maintaining a survivable second-strike capability with nuclear weapons, now under the United States Strategic Command.
Communicating with submarines
Normal radio waves cannot penetrate the ocean to any significant extent, which presented a major challenge for sending nuclear strike orders from the National Command Authority to the missile submarines, which stay quietly submerged and, as far as is known, undetectable. It was determined that Very Low Frequency (VLF) radio could penetrate deeply enough to serve as a "bell-ringer" for a submarine. The VLF message told it to rise to a depth where it could raise, while still submerged, a hard-to-detect antenna that could connect to a higher-speed source of message traffic.
One of the challenges of VLF is that the transmitter needs to have an extremely long antenna. Land-based VLF stations were enormous, and easy to disable at the start of a war. In 1963, a Marine Corps KC-130 tanker aircraft was converted into a EC-130, carrying a VLF transmitter. By staying in a constant gentle turn, the aircraft trail an appropriate wire transmitter to send the necessary VLF communications. The aircraft, of course, could easily receive air and satellite communications telling it to relay the VLF signal. The mission was called "Take Charge and Move Out", or TACAMO.
Eventually, the KC-130s reached the end of their service lives, and a replacement was necessary. The original approach was simply to use a (relatively speaking) newer aircraft, based on a reengined Boeing 707, to replace the turboprop C-130 derivative. This new communications platform was the E-6A.
SAC Airborne National Command Post (ABNCP)
Through much of the Cold War, the Strategic Air Command (SAC) conducted the LOOKING GLASS mission, which kept an EC-135 aircraft continuously in the air; one never landed until its replacement was operating. This aircraft carried an Air Force brigadier general and a minimal battle staff for ordering SAC B-52 and B-47 bombers, as well as intercontinental ballistic missiles, to carry out Single Integrated Operational Plan missions.
There was no known way to interfere with the commands from a constantly moving airborne command post, hardened against electromagnetic pulse. While the details remain highly classified, it was accepted that the LOOKING GLASS general, on either receiving a command from the National Command Authority, or confirming that all other command posts had been destroyed, was the lowest-ranking officer who could order an American nuclear attack.
The EC-135s were aging as well. It was realized, however, that it was entirely feasible to upgrade the E-6A to carry the battle staff of LOOKING GLASS, and thus need only one "doomsday aircraft". 
The merged solution
The E-6B Mercury aircraft carries out the TACAMO and LOOKING GLASS strategic mission, modified for the post-Cold War environment. They are organized in Navy Strategic Communications Wing One, which is housed at Tinker Air Force Base, Oklahoma. Tinker is also the home for the Air Force E-3 Sentry tactical airborne warning and control aircraft.