Basically, it adjusts the attitude rating based on the smaller of the two WarmongerRespect settings of the two civs in question.
In base civ, since everyone is either 2 or 0, what happens is that those with a 2 rating get +2 attitude towards each other. No effect for anyone else.
If you start changing things around so that some have 3, some 1, etc, then you end up with a bit more complex relationship.
Also, Warmongers are less likely to vote to ban nukes.