Jesus assured His disciples that it was to their advantage that He go away so that the Helper could come (John 16:7)--God sends Him to convict people of their sin. Since the Holy Spirit is unlimited by time or space, He can reach out to every individual on the planet. However, His work differs with regard to believers and unbelievers.
With regard to unbelievers, God's Spirit penetrates the heart and brings awareness of wrongdoing. He reveals that according to God's holy standard, they have sinned and stand condemned by their transgression. Unbelief is the greatest sin against God, so every prick of the heart is meant to point out their need for the Savior.
As for believers, the Holy Spirit deals with them on the basis of their relationship with Jesus Christ and convicts us of disobedience to Him. In other words, He makes us aware of specific sins and the Lord's attitude about them. But He also prompts us to be accountable before Christ for our wrongdoing by confessing it and repenting.
Convicting believers of sin is an important part of the Holy Spirit's job, but He is equally delighted to make them aware of the Lord's approval. God commends righteous living, obedient actions, and loving acts done in His name.
While conviction is often uncomfortable for unbelievers and believers alike, it's a beautiful demonstration of God's love. He desires to bring us into the center of His will and keep us there for our good and His glory. The Holy Spirit's work makes that possible, if we choose to follow His promptings.