Projects are tasks to complete that will give you rewards, depending on the task.
Talk to the projects officer to see them and donate the required items. You can also see them in the map.
Each district has a liberation project, once you complete it, you get a bounty to do. The bounty is on a timer though, you have to get to the place of the bounty within a certain time. Once you are there, the timer stops.
Downtown East Liberation
Resupply a friendly control point in Downtown East: 50 Complete activities in Downtown East: 3 Recover SHD Tech caches in Downtown East: 4
Outfit Hunting Party
Steel: 5 Chest armor: 1 Neutralize hostile activity: 1
Rewards: Blueprint: Streamlined Iron Sights, 645 XP
Polycarbonate: 5 Gloves: 1 Disrupt Public Execution: 1
Rewards: Blueprint: Vertical Grip, 645 XP