To roil means to stir up or churn. A stormy ocean might roil, or even a restless crowd.
The word roil is often confused with rile, which has a slightly different meaning. If you roil someone you're stirring them up but not necessarily annoying them. To rile someone is to deliberately provoke or antagonize them. Usually there's no roiling without riling. Muhammad Ali roiled much of America when he refused to be drafted for the Vietnam War.