Influence is how you rate yourself against other players in PVP (player versus player).

You lose and gain influence points by raiding enemy outposts and defending your own, depending on your performance. You can see your amount of influence points in the outpost building.

Points are calculated for the duration of a cycle, after which you receive a reward based on your rank.

While you can gain influence by winning raids, you can win more by facing and defeating opponents with higher influence scores than you have.

If you have a very high influence score, it can be challenging to find an opponent with an even higher score, and the rewards will be scaled accordingly. It's a hard life being the best!