It's a form of fasting. (A very wimpy, watered-down, and easy-to-observe form of fasting, but a form of fasting nevertheless.)
Christians have fasted since the earliest days. Christ commends "prayer and fasting" to drive out demons, and himself fasted in the desert for 40 days at the beginning of his public ministry. The Didache (ca. AD 80) commands fasting on Wednesdays and Fridays. Fasting is a form of self-denial and mortification. There are whole books written on fasting and other spiritual disciplines. A simple explanation of "why should I fast" is that, by fasting, you voluntarily give up some created natural good to remind yourself to focus on supernatural goods: God and intimacy with him through grace.
I just don't understand why if I fast at a time specified by another, how that really ever relates to me or my personal communication with God.