The Holy Spirit convicts the world of sin, of judgment, and of righteousness. The fist step, is convicting of sin.
Take Paul for example...He was convicted of sin on the road to Damascus. Paul thought he was doing God a service and working for him by persecuting the Christians.
However, what did Jesus say to him? Saul, Saul, why persecutest me? In this, Paul was convicted of his sin. The truth and his sin was laid bare before him.
This is conviction of sin, and the Holy Spirit does this for the whole world...
So can you see how, this God working in everyone to show everyone the truth. He convicts the world of sin, of judgement, and of righteousness. He let's us know that we need a Savior. Now, that does not mean that he is going to make everyone accept it, but the Holy Spirit convicts the whole world. No one will have an excuse.