To incite is to cause to act or occur. Violent words can incite violent actions which, in turn, might incite public outcry against violence.
Incite comes from a Latin verb meaning "to move into action" and if you incite someone to do something, that is exactly how to describe it. Usually it is used in a negative context. Radical and intolerant teachings can incite hatred in those who listen. And if a government restricts its people too much, it can incite unrest and rebellion in the population.