Expedition mode is basically a PvE mode. It can be accessed at the 'Main' menu by tapping the 'Menu' button located at the bottom-right corner of the screen. Expedition mode has 70 stages and although you can play the modes stages multiple times a day the maximum reward you can earn from it in a day is 300 Medals.
It is advised that you participate in Expedition mode daily so you gain the type of rewards that can be exchanged for Commander Sculptures in the Medal Store. Commander Sculptures are used to upgrade your Commanders and unlock various new Skills. To visit the Medal store go to Expedition mode and tap the shop icon located at the top-right of the screen.