The Adepts were the humans who first rose up against The Watchers hundreds of years ago. They were victorious in this regard, and sent the Watchers to the Void as punishment for their enslavement of humanity.
According to Atem, every human has something special inside of them, but many choose not to utilize this special something of theirs. The Adepts are those humans who are able to tap into these special abilities, which (among other things) allows them to fight better whilst in combat.
According to background info revealed in the game's loading screens, the Adepts continue to very covertly resist the Watchers plans on Earth to this day (which, in game time, would be 1938).