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 2067, mostly since 2236. The Enclave is pretending to still have authority over the wasteland, 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 inferiors, if not mutants, and need to be eradicated.
In the pre-war period, the persons considered as the United State's elite were mostly in favor of a nuclear war, and actually knew no one would survive to it, except them. During the Great War, while the common men and women were protected in Vaults - that were rather a social experiment - the Enclave members and the government's families went to secret shelters, one of which was the Poseidon Oil Rig, that would later become the Enclave's main base.
Later, when its forces were strong enough, its soldiers gathered in the Oil Rig and, with its technology better than anything else in the wasteland, Enclave started to scout the wasteland, to gather slaves for experiments, gather information and try to seize control of small areass, like its secondary Navarro base.
Enclave's technology is the best in the whole wasteland. Its armors are stronger than the Brotherhood of Steel's, as it has the powerful Advanced Power Armor and most of the strongest weapons including vertibirds, the only flying object in Fallout.
The Enclave's only problem is its limited manpower, as it often lacks soldiers. However, they don't take many casualties since their armor protect them well, and they are careful not to take many risks.