Most missions have specific requirements about an item's type and power (Gear Score). The requirements are explained in the top-right side of the pre-mission menu.

If you don't have the required item type, or an item isn't powerful enough, you can't start the mission.

If the mission is part of a Street Cred Event, you can use Event Items to both access Event Missions and speed up your progress. For City Events, such as Portals, you don't have to have specific items -- event missions provide all required gear for the duration of the mission.