Mortification of the flesh literally means "putting the flesh to death". The term is primarily used in religious and spiritual contexts. The institutional and traditional terminology of this practice in Catholicism

Catholicism

Catholicism is a broad term for the body of the Catholic faith, its theologies and doctrines, its liturgical, ethical, spiritual, and behavioral characteristics, as well as a religious people as a whole....

 is corporal mortification.
The term "mortification of the flesh" comes from Saint Paul

Paul of Tarsus

Paul the Apostle , also known as Saul of Tarsus, is described in the Christian New Testament as one of the most influential early Christian missionaries, with the writings ascribed to him by the church forming a considerable portion of the New Testament...

 in this quote: "For if you live according to the flesh you will die, but if by the Spirit

Holy Spirit

Holy Spirit is a term introduced in English translations of the Hebrew Bible, but understood differently in the main Abrahamic religions.While the general concept of a "Spirit" that permeates the cosmos has been used in various religions Holy Spirit is a term introduced in English translations of...

 you put to death the deeds of the body you will live.".