Vengeance is a status that can be received when a player who has a yard of much lower level (at least 3+ levels) than yours that attacks you. It will last 24 hours from the time the player attacked you. During that time, you will be able to attack the player who attacked you as many times as they attacked you, despite their low level. This is only effective on Level 1 Map Room; this does not apply to base or outpost at level 2. However, some high level players on Map Room level 1 think that it is a waste to use their vengeance to attack the low level players because they don't provide much resources. These low leveled players are also not able to steal that much from the higher player's base because their monsters are still weaker to attack.
For Example: Player B is Level 27. He attacks player A who is level 32 (level difference is high: 3+). After that, player B logged out and then player A logged in. Player A has now vengeance enabled 1x.
"Normally you wouldn't be able to attack a person whose level is so much lower than yours, but they were dumb enough to attack you first! We'll let you attack them as many times as they attacked you to teach them a lesson. As they say, 'Revenge is a dish best served cold.' "