Penance is an act of conversion.
Conversion is turning away from sin and turning towards God. The first conversion we receive is at the Sacrament of Baptism. Post Baptism, conversion is an ongoing process that we can achieve through prayer, receiving the Eucharist, going to confession, fasting, etc.
An example of conversion is the story of the Prodigal Son. (Luke 15: 11-32)
The Father represents to us God. He forgives his son immediately and unconditionally.
The Prodigal Son is the example of conversion because he turned away from sin toward God.
The older, more well-behaved son teaches the value to us of maintaining a relationship with God everyday.