Scenario Distributions allow map creators greater control over how territories will be distributed at the start of a game. For example, in the Double Earth map, a scenario is defined called Top/Bottom that forces one player/team to start on the top half of the map and the other player/team to start on the bottom. To accomplish this, the map creator simply defines a Scenario Distribution with two scenarios: Top and Bottom. They then add territories from the top into the Top scenario and territories from the bottom into the Bottom scenario.
When the game begins, each player/team is randomly assigned a scenario and will start entirely in that scenario. Teams are always assigned the same scenario. The scenario each player was assigned is visible in the Players Panel.
Scenario Distributions are useful for more than just mirror maps. For example, a map creator could create a World War II map where one player starts as the Germans and another as the United States. In this case, Germany would be one scenario and the United States another.
If scenarios defined in a map are different sizes (i.e. contain different numbers of territories), it is possible for players to end up with different number of territories at the start of a game. This can be circumvented by game creators by using the Limit functionality, however it is up to the map creators to ensure their scenarios are well-balanced.
Note that scenario distributions and wastelands don't mix well. Since wastelands are randomly distributed, one player/team may end up with more wastelands in their area than others. For the fairest game, turn off wastelands or use custom scenarios to place the wastelands fairly.