Expedition game mode lets you send your characters on a journey to get Herostones, Gear and other items.

As the reward for the Expedition you also get a Guiding Star. Guiding Stars are required to increase the Expeditions levels.

The higher the level, the higher the chances to send your heroes on an Expedition of a higher rarity level.  
The higher the rarity of the Expedition, the more stars it gives, and the more valuable reward you can get.