From the Metal Gear Wiki

Outer Heaven refers to several different things in the Metal Gear series. It was an idea, military company and fortress built by Big Boss. The inspiration for Outer Heaven came when Gene revealed his treacherous plans of using and exploiting soldiers, Big Boss thought up the philosophy of Outer Heaven as a response to Army's Heaven.

It was the early 1990's. Big Boss had established a mercenary company known as Outer Heaven, and through it, aimed to create and control Wars, this in return would increase the sphere of soldier's usefulness and the world would require soldiers, which would be provided to them by Outer Heaven. He was also carrying a black project of his own in Metal Gear TX-55. A bipedal tank capable of launching a nuclear strike from anywhere on the planet. Outer Heaven intended to use Metal Gear to destroy the balance of nuclear deterrence, and become the world's sole superpower and achieve Global Military Domination. Outer Heaven as a place was a gigantic, impenetrable fortress 200km north of Galzburg, South Africa.

However in 1995 during Operation Intrude N313, rookie FOXHOUND agent Solid Snake infiltrated Outer Heaven, and succeeded in rescuing the missing agent Gray Fox and destroying Metal Gear. Big Boss then confronted Snake, activating Outer Heaven's self destruct sequence, hoping to stall Snake long enough for him to kill Snake in blast (seeing as how Big Boss managed to survive not only the battle with Snake but ensuing explosion as well, it is safe to assume he had some sort of escape passage.)

Then in 2005, during the Shadow Moses Incident, rebelling members of FOXHOUND took over Shadow Moses along with the GENOME Army, and threatened the rest of the world with a new Metal Gear, Metal Gear REX. To honour Big Boss’ dream and memory, Liquid Snake changed the name of Shadow Moses to Outer Heaven. This plan was also thwarted by Solid Snake.

Solidus Snake then used the term in 2009 as a code-name for his plan to take control away from The Patriots. His plan consisted on giving Arsenal Gear to Dead Cell operative Fortune, who Solidus knew would attempt to challenge the Patriots. Then, using her as a distraction to lure The Patriots fire, Solidus would detonate a nuclear warhead over Wall Street, which would act as a gigantic Electro-Magnetic Pulse over an entire area of America, taking control away from The Patriots. Solidus would then go on to eliminate the Patriots one by one. This plan, however, never came into fruition and by the end of the Manhattan Incident Solidus had been killed by Raiden.

[edit] Outer Haven (PMCs)

Liquid Ocelot (Leader of Outer Haven PMCs) used the term for the final time in 2014 as a name for his “Mother Company” which he had set up to control five-large PMC companies. Liquid is the new leader. This was Liquid’s way of capitalizing on the way war had become a large Economic property in the 21st Century. Presumably, Liquid was doing this in order to plunge the world into a complete World War, much in the same vein as Big Boss’ original vision. Each of the PMC Companies went code-names, one was known as "Praying Mantis", another "Outer Haven" and Liquid's personal Army was known as the "Frogs".

[edit] Army’s Heaven

Army’s Heaven was an idea created by Gene. Gene had collected funds, resources, men, and had the plan to build Army’s Heaven and control the world from the underground (much like The Patriots do). By the time of the FOX Unit’s Rebellion in 1970, he quickly devised a plan to make Army’s Heaven with the use of the FOX unit members and Red Army soldiers.

During the San Hyeronimo Incident, Gene’s plans of becoming the Ultimate Leader and Guide of the world was dissipated when Big Boss fought against him to clear his name, and stopped him from launching Metal Gear into America. Before their battle commenced, Gene told Big Boss of Army's Heaven. According to Gene, humans were fragile creatures and they need someone of superior will to give them a calling. Compared to his mission, individual will of individual soldiers were meaningless. Big Boss never agreed with this philosophy. Big Boss said that he uses fear and deception to keep his soldiers in line, and he exploits them. Big Boss also said that soldiers were looking for place outside his heaven. Outer Heaven was created as an opposition for organizations like Army's Heaven. A few decades later, Outer Heaven gave soldiers a place to fight, and a battlefield to survive. This explains why Big Boss wanted a never-ending war. So that soldiers will always have their purpose of existence, that is War.