Personal discipline can be correlated to spiritual discipline. Fasting recognizes this as a matter of principle and attempts to bring the two together. Through fasting, one clarifies that the spiritual and the physical cannot be separated in a Gnostic sense while at the same time prioritizing spiritual concerns over material ones. Fasting essentially says to oneself and to God that the spiritual concerns which led to the fasting are more important, at least for the moment, than other needs or wants. It can therefore be viewed as a sort of personal sacrifice, or self-denial, after the model of Christ who said, “If anyone would come after me, let him deny himself and take up his cross and follow me” (Matthew 16:24 ESV).
For one of the best discussions of fasting I have read in a while see this great post: The Gift of Fasting.