Influence is an important property of towns. Every town has a maximal influence value that depends on its Town Hall level only and a current influence.
The current influence is always in the range of 0 to the maximum influence. It goes down if the town gets attacked successfully (at least 1 star). It regenerates by 10 every minute. There are also items to increase influence by 1000 or to its maximal value. Those can be won in the casino or bought from the shop. If influence of a town drops to zero, the town gets ported to a random location on the realm and the player gets a free advanced teleporter. The first 12 hours 30 minutes after a teleport (forced or by the player), the town recovers influence at an increased rate of 200 every minute. That recovers 150000 influence - enough for town halls up to level 9, and 3/4 of the max influence for level 10.
Depending on the town hall level, the town "needs" some area on the map (the tiles around the own town). Higher levels need a larger area. If the influence is below the maximal value (or below 145000 for town hall 10), the town "loses" tiles (marked with a ":(" on the map for the own town, unmarked tiles for other towns). If a player nearby without alliance or from another alliance (not friendly) tries to occupy the same tiles as the own town, there is a border conflict and those tiles gets red. Both types of tiles are temporarily lost for the town: the production is reduced if a town does not have the maximal area for its TH size. The formula: Production = MaximalProduction * (blue tiles) / (max tiles it could have).