The Enclave is one of the most powerful organizations in Fallout, if not the most powerful. The Enclave presence was revealed to the world only in year 2242, even if it has done many operations since the Great War, mostly since 2236. The Enclave claims to still have authority over the former United States, as it is composed mostly of descendants of pre-war government or elite soldiers. To them, people born outside of the Enclave's bases are inferior, if not mutants, and need to be eradicated.
In the pre-war period, the persons considered to be the United State's elite were rather for a nuclear war, and actually knew no one would survive it, except them. During the Great War, while the common men and women were protected in Vaults - that actually were built as a social experiment - the Enclave members and the government's families went to secret shelters, and one of them was the Poseidon Oil Rig, that would later become the Enclave's main headquarters.
Later, when its forces were strong enough, its soldiers given professional military training and its technology better than anybody else's in the wasteland, Enclave started to scout the wasteland, to gather slaves for experimentation, gather information and try to seize controls of small areas, like its secondary Navarro base.
Enclave's technology is the best in the whole wasteland. Its armor is stronger than the Brotherhood of Steel's pre-war variant of Power Armor, as it has the powerful Advanced Power Armor, the most advanced weaponry and, of course, the vertibirds, the only flying object in Fallout.
The only problem of the Enclave is its manpower, as it lacks the territory and resources to create a large manpower pool. However, Enclave units take very little casualties due to the advantages mentioned above.