Kevin DeYoung explains what this activity of the Holy Spirit looks like:
The Holy Spirit acts like a giant searchlight, exposing the world's wickedness and calling people everywhere to repentance. It's as if the world is having a nice romantic candlelight dinner, thinking everything is sirloin and roses, and then voila! The Spirit flips on the lights to expose cockroaches scurrying up the walls and garbage strewn about the floor. We are not as good as we imagine, and the Spirit can prove it to us.
In the Gospel Coalition pamphlet, "The Holy Spirit"