From Haug & Walker's Journey to the Cross:

"One of the ways we identify with [Jesus'] suffering is by practicing self-denial. Whether it's food or TV or 'me-time,' we deny ourselves particular comforts and pleasures as a way of remembering what he endured. The point is not to manufacture suffering as if we could earn some kind of righteousness through self-denial. Our [purpose] ... is simply to de-clutter our self-absorbed lives."

Jesus did this in the wilderness. He spent forty days eating nothing, preparing His soul for His ministry. The goal of depriving Himself of food was to direct His longings to His Father. Haug & Walker go on:

"'The devil said to him, "If you are the Son of God, command this stone to become bread"' (Luke 4:3). Certainly Jesus could have done this, but the lack of bread revealed a deeper hunger for God, and a deeper satisfaction of being sustained by God."