The Catholic Church teaches that penance is intimately bound-up to the Catholic understanding of sin.
The Catechism of the Catholic Church provides a perfect summary of penance and its connection to sin.
In this case, penance is the word that describes our actions to repair the damage left by sin.
Typically this definition of the word is tied to the sacrament of penance, whereby a priest will prescribe a penance to make amends.
This is the most common understanding of penance, though sometimes saints will explain how they would go above and beyond what the priest prescribes and impose a "personal penance."
For example, a saint may explain how they always slept on the floor as a penance for their sins or weaknesses. Their confessor didn't suggest that they do that, but the saint may do it anyway, so that they can join in the suffering of Christ on the cross.
Normally they would only engage in such actions under the guidance of a priest, who would make sure their actions weren't harmful to their body or soul.
The key to the Catholic meaning of penance is that it is an action done in reparation for sin, with the intention of restoring our relationship with God and our neighbor.
