The Conspiracy is Sombra's name for an unknown party with ties to people and organizations across the world.

Sombra came close to finding the Conspiracy and was attacked for it, forcing her into hiding. After joining Talon, she continued her search to find out who they are, and how to exploit their weaknesses.
Why and how are they connected to so many people? What is their goal? What did Sombra find out before she was attacked? No one ever speaks of them and yet they're the game's main antagonist it would seem.