Stagnation is a term used to indicate an Empire which has no room for expansion. If the Empire's colonies and Homeplanet are all filled up, then the Empire is stagnant. Quite often being stagnant will lead to boredom of the game, as no growth means one less target and your allies and enemies tend to overtake you.
Stagnation occurs somewhat differently in redesign universes, since they have no maximum on the number of colonies. New levels of Astrophysics Technology (required for more colonies) will get very expensive over time, so the stagnating effect, that of diminishing growth and the boredom linked to it, can still be experienced. There is a practical limit of planets when Astrophysics technology begins to take more than a month and billions of resources to complete, which makes it unprofitable to get more than 12 or 13 colonies and impractical to get more than 15.