The maximum desired population is the number at which the storyteller will try to keep you at. That happens when you started a game with less than the minimum desired population defined by the storyteller you chose. You probably noticed that you usually get an escape pod and potential new colonists pretty soon in the game.
The minimum desired population is the minimum population the storyteller will aim to give you. There is no limit to the number of people you can have in a single colony, but each storyteller has 3 variables that affect the population in your colony: minimum desired population, maximum desired population and critical desired population. The first thing you need to know is that the amount of colonists you have in your colony is strongly influenced by the storyteller you chose when you created the game.
