"Mortification" is the act of dying to oneself by killing off the sinful desires of the flesh as taught by St. Paul:
Romans 8:13-14
For if you live according to the flesh, you shall die: but if by the Spirit you mortify the deeds of the flesh, you shall live. For whosoever are led by the Spirit of God, they are the sons of God.
Galatians 5:18-25
But if you are led by the spirit, you are not under the law. Now the works of the flesh are manifest: which are fornication, uncleanness, immodesty, luxury, Idolatry, witchcrafts, enmities, contentions, emulations, wraths, quarrels, dissensions, sects, Envies, murders, drunkenness, revellings, and such like. Of the which I foretell you, as I have foretold to you, that they who do such things shall not obtain the kingdom of God. But the fruit of the Spirit is, charity, joy, peace, patience, benignity, goodness, longanimity, mildness, faith, modesty, continency, chastity. Against such there is no law. And they that are Christ's have crucified their flesh, with the vices and concupiscences. If we live in the Spirit, let us also walk in the Spirit.
Mortification is practiced by doing what all Christians must -- fulfilling our duties, no matter how unpleasant; avoiding near occasions of sin (those situations that tempt us to sin); denying ourselves that which is evil, etc.
It can also mean voluntarily taking on unpleasant things that aren't a matter of duty or of directly fighting off evil habits, but which simply subject the flesh in order to increase humility, express contrition, and build up the Body of Christ. These acts of mortification can include offering to God small acts, such as: fasting or practicing abstinence when not bound to; denying oneself an ordinary pleasure simply for the sake of God, such as giving up cream or sugar for your coffee for a time; taking on an unpleasant task one isn't bound to take on; sitting on the hard chair rather than the soft one, etc. And they can include offering to God acts that appear (to
These sorts of external voluntary mortifications that aren't a matter of duty and which don't fight an evil habit directly are only beneficial insofar as they arise from the desire for humility, for penance, and to build up the Body of Christ, and insofar as they actually do lead to humility and penance. More extreme forms of mortifications should only be practiced with the guidance of a good spiritual director.