Exploration is basically a dice rolling game that will allow you to gain increasing rewards during the event period. You earn fuel from the campaign and war in order to perform the exploration. When the event period ends, any leftover fuel becomes contaminated and cannot be used for the next exploration event. You can open them for 50,000 gold.
How to Explore
Once you've gained enough fuel to start an exploration you can click on the event icon on the main main menu.
Now you can start your dice roll. Click go and wait for the results.
You will be given two numbers, if they are the same then you get a free roll. Either way you get to select how many steps to take. Watch out for the trap icon. This will transport you X number of steps forward or backwards, which could be a good thing if there's a reward that you passed you might want. However you don't get a choice in where it sends you.
As you complete zones the fuel costs increase. Also as when you finish a zone you get to keep drawing rewards until you draw an X, with a potentially great amount of rewards to be gained!