If you go to your guild window and click on the Level tab, you will see what level our guild is, how many Guild Power Points we have accumulated toward the next level, how many Guild Power Points are needed to reach it, and the bonuses/boosts guild members get at both the current level and the next. These crowns are actually Guild Power Points. A popup will show you how many crowns your guild has been awarded and how many you will get at the next level.
The number refers to how many levels of crowns you have reached. Beside it is a crown icon with a number superimposed over it. The running total/total for next level of crowns is on GE screen. As the total grows, it attains certain numerical levels that increase the number of crowns that the guild receives. They are added to our guild’s running total. For each encounter, you get Expedition Points. You clear encounters by battling/negotiating.
This is the excerpt from our guild forum but doesn’t really touch on the GE Championship.