To be “convicted of sin” is a spiritual phrase. Conviction as a word has 2 meanings: it can mean, first, to be completely convinced of something; and second it can mean to be found guilty in a court of law. Conviction of sin carries both of these meanings.
A person who is convinced by God that they are wrong about something is said to feel conviction. When an unbeliever comes “under conviction” then that person sees the totality of their sin nature and feels the hopelessness of remedy. Conversion is often preceded by conviction.
Jesus said that he would send the Holy Spirit to his followers once he got to heaven. He said that the Holy Spirit would “convict the world of sin”. It is God’s will that humans find forgiveness. Usually though they first have to see their need of salvation. To come under conviction can be a terrifying experience. Its purpose though is for good, since only by being deeply convicted of sin can a person fully turn to God.
Now, believers too can still feel conviction even though they are forgiven. When the Holy Spirit “leads us into all truth” He leads us, among other things, to see our sin. We can see both individual sins and global areas of wrongness within us. These processes are valuable because they produce contrition, repentance and sanctification.
Many people suffer incapacitating guilt because they confuse conviction with accusation. For a person to merely feel guilty about something does not mean that they are feeling conviction. Accusation is false conviction. It is an attempt to bring a sense of wrongness to something that is not really wrong. We need to test our experiences, measuring them against reason, scripture and counsel. Our conscience may need to be educated and reformed too.
Some Christians progress all the way through a process of conviction and education and yet still feel a sense of disqualification because they continue to see wrongness within them. We are supposed to see the continued presence of sin within us, because we need to see that we have a dual nature, with both sin and God within us. We need to see both the new man and the old man. When we resist the sin within us and yield to God we complete our justification and move through the process of sanctification. Being convinced that I have inherent sin within me is meant to produce humility and dependence on God, not guilt. Guilt comes when we yield to temptation and thus obey our lower nature. Merely having a lower nature is not a sin. A child of God is pleasing to God both because of an imputed righteousness, and because of a maturation through obedience into holiness. Conviction then ultimately leads to peace and life and union with God.