Penance is the actual name of the Catholic Sacrament of Reconciliation/ Confession. In this Sacrament, the penitent (sinner) accuses himself of his sins to an ordained priest. The priest may then offer advice and imposes a particular penance to be preformed. The penitent then prays an Act of Contrition, the priest administers absolution, thus formally forgiving the penitent of his sins, and finally sends him out with words of dismissal.
Penance, as imposed during the Sacrament, may consist in prayers, fasting, or the giving of alms. The most common penances are prayers, such as an Our Father and Hail Mary.
Penance also may be self-imposed, as during the Lenten fast and Advent. Self-imposed penance, also called mortification serves to detach the penitent of his worldly passions, as to draw him into closer union with God.
In eastern religions (Hinduism, etc.), acts of hardship committed on oneself (fasting, lying on rocks heated by the Sun, etc.) in order to attain a higher form of mental awareness or favours from the Gods.
Penance is the name of an extremely powerful optional boss in Final Fantasy X. It appears to be a machina that appears after the ten Dark Aeons, who are also powerful optional bosses, are all defeated. It boasts the in-game record of 12 million HP, high stats, elemental absorbtions and powerful attacks, making it what might be considered the most dangerous boss in the game. It is accompanied by its two arms in combat which have their own powers, including regenerating a couple of rounds after defeat. Defeating this beast of a boss can take around one full hour, and that's if you're fast. In terms of overall power, it makes the final bosses of the game look pathetically weak. Despite it being the single most powerful enemy in the game, it can probably be felled by the Zanmato attack used by the aeon Yojimbo.