Popularity affects play according to the following chart:
0%-25% popularity: Rebellion, either open or routinely and brutally suppressed. They will actively aid invaders in your lands.
25%-50% popularity: You are an unpopular lord, and order is maintained largely by your soldiers. Your people may shelter rebels, but are unlikely to be in rebellion themselves. Your people are very vulnerable to populist demogogues and the influence of the pulpit at the Church. They are unlikely to take sides if your lands are invaded.
50%-75% popularity: While you are not loved by your people, neither are you hated - and while your soldiers are required to maintain order, they do so by their presence more than by their actions. Those who shelter rebels in your lands are unlikely to be given up to your rule, but by the same token most doors will be closed to rebels and criminals. Your people are very attentive to the word of the Church, and are also somewhat vulnerably to populist demagoguery. They will resist invasions that are not sanctioned by the Church, the Emperor or by a popular independent lord.
75%-100% popularity: You are a popular lord, and your people are not only unlikely to rebel they may even point out rebels to your soldiers. Still, particularly charismatic populists or the Church can rile your people up against you. Your people will resist anyone who tries to invade your lands unless they have the sanction of the Church or (at lower levels) the Emperor.
100%+ popularity: You are beloved by your people, who will defend you even against the Church should they come for you.
Events and Popularity
Like loyalty, IC events affect popularity. Here are some examples - again, they can vary by house.
+5-15% Church favor. The Li Halan tend to be 5-10% and clergy at 10-15%. +2-5% Routine association with peasants +5-10% Favor from populist leaders +2-5% Favor from guild leaders -2-10% Rampant crime -5% Public criticism from the Church -10% Public condemnation from the Church -15% Excommunication or interdict -5-10% Opposition from populist leaders -5-10% Natural disasters and acts of the Pancreator -2-5% Bad omens