Hate is a numerical representation of how angry a military Settlement is towards a player's dungeon and how likely they are to retaliate. Hate is specific to a dungeon meaning that even if a player's starter dungeon may have generated a lot of hate from a particular settlement, their expansion dungeons will not.

Hate button
To check a particular settlement's hate, select the settlement on the Overworld map and then click the hate button. Military settlements display a message in the format of:

Dungeon Name: #% Reprisal Chance (Hate ###)
Example: Hades: 2% Reprisal Chance (Hate 769)

Non-military settlements do not gain hate, but rather list all of the military settlements that will gain hate should they be attacked.

Hate is generated through the raiding of Settlements. The more time a particular settlement is raided, the more likely a protecting military settlement is to retaliate. For discussion and theory on how hate is actually generated see Hate Generation.