Buffs are empowerments that raise or lower specific values.

On the one hand, you can build buff buildings, which will influence a certain value of your castle (e.g. School - Production Rate). Those buff buildings will influence their values even more when being upgraded.

On the other hand you can get buffs by conquering a Fortification with your alliance. All members of that alliance will be influenced as long as they are in it's buff range. The values influenced depend on the kind of Fortification conquered and its level.

Also, thirdly, you can "drink" brews at the tavern. There are brews representing each damage type, raising that types values to a certain level for a certain amount of time.

Fourth, and probably most permanent, are the researches. They increase or lower specific values and can not be reversed.