This is one of the key missions that Luke outlines in his Gospel. Here, Jesus goes on to affirm not only that He is willing to identify with cultural outcasts and confessed sinners but also that this is the very reason why He came. In His ministry, He does not seek to gather the righteous but rather to invite the sinful, lead them to repentance, and make them righteous.
Pharisees criticized Jesus for eating with sinners, unaware that God saw no difference between the self-righteousness of the Jews and the unrighteousness of the tax collector. A person's repentance is the act of turning from sin, and the act of turning from sin can only lead to one's turning to Christ Jesus, the propitiation for one's sins, our only Savior, and the only Mediator between man and God.
No matter how good we may think we are in comparison to other people, we are all sinners, having fallen short of God's standard and in need of a Savior. No matter how bad we think we are compared to other people, Christ has already paid the price for every sinner. Only in Christ do we find forgiveness. Only in Christ do we find eternal life.

Dear Heavenly Father, thank You for Your wonderful plan of redemption. You looked down on humanity's sin and sent Christ Jesus to call sinners to turn from their sins and trust Him as their one and only Savior through grace. I pray that You will use me to lead them to Your blessings and to help them find their family with Your people. 
In Jesus's name I pray. Amen.