From Destinypedia, the Destiny wiki
Catalysts are special modifiers for Exotic weapons, introduced in the Warmind Expansion for Destiny 2. They improve and upgrade Exotic weapons within the game by either improving stats, giving bonus perks, or raising the magazine size.
Each weapon has its own Catalyst and has specific objectives to find them. Catalysts function exactly like Masterworks and generate Orbs of Light on multi kills. The drop rate for them is unknown, but they are a rare find. Once you find a Catalyst for a weapon, you will have to do specific objectives with the weapon, such as precision hits or simply kill enemies in order to unlock the upgrade.
List of Catalysts
List of Appearances