Expeditions are end-game content.
To unlock them, you need to complete the story line of the game.
After that, you'll be able to complete expeditions (I won't tell you what is the story behind expeditions because it will spoil the game).
You basically need to kill 1.000 in those end-game missions
As @yzmyyy stated, it should take around 5 or 6 expeditions to complete.
Each expeditions is 10 to 15 minutes long