There is some hidden stats on regions in the game and this is one of them. Popularity drops when you hold harsh courts, brutal and hostile (?) takeovers and when your realm loots the region or any adjacent region. Presumably there are other factors that involve it as well.
It can be repaired (slowly) by civil work in the region, festivals in the duchy and I think by holding just and perhaps also merciful courts. Diplomats and courtiers can probably be helpful as well but I don't really know about them...
