Progression Points are used to unlock new helicopters, their modifications, and camouflages. They can be earned by doing positive actions in any online battle: deploying soldiers, destroying enemy targets, scouting, etc. Rewards for some actions depend on a number of players in battle (e.g. capturing LZ).
Due to technical restrictions, you can’t earn progression points in offline mode. However, if you would like to play alone, join a server, start PvE/Co-op battle, and set a password. Nobody will be able to join your game while you still will be receiving progression points.