Province morale represents the population’s collective willingness to fight for your nation, and is directly tied to the construction and production speed of the province, as well as its resource generation.
If province morale drops below 30%, the population may rebel against you. Stationing troops on the province centre can help to protect against the rebellion, but you must ensure that you have enough troops on duty - as small garrisons can be overpowered or may defect and join the rebels.
A province that rebels will choose another nation to join - this may be an enemy that you are currently at war with, or it may be a neutral nation that has not been involved in any of your conflicts. They may also join an allied nation.