What does it mean to deny yourself?

Mother Angelica put it this way,

“When you do penance for Lent, you imitate Jesus, and secondly you strengthen your will so when something sinful comes your way, you can say no. See, there’s a two-fold advantage to doing penance. Real penance, not giving up candy for goodness sakes. . . . If you gave something up that costs you, not money, but something in here, then by the end of Lent you’re stronger. Your will is stronger to say no to more important things.”

Mother Angelica Live, March 7, 2000