Honor is a player point system that is a factor to determine your rank within Evony.
You can gain honor by attacking or defending locations and loosing less troops recource-wise . If you have been attacked (even on Valley), returning the attack on the city that attacked you can result in a rise in Honor (defending what was taken)
Attacking a city or city’s valley when they have been declared a hostile alliance to your alliance can result in higher honor if you lose less recource in the battle.
You lose honor by continuing to attack a location and loosing more recources than the other player. You can also lose honor by attacking or defending against a player whose rank is much lower than yours.