Fasting facilitates entry into low level non-ordinary states of consciousness. It allows the person fasting to connect to the world around them differently than an average day of eating. Fasting shows restraint, and when an adherent couples that restraint with devotion it is a powerful symbol of one's dedication in spite of the limitations and exigencies of the physical, material world.
Fasting is a practice observed by religions the world over. for some it is a mater of devotion by protesting the flash, for others it is an exercise in humility. Both serve to humble the flesh to elevate the mind. In other religions water fasting is utilized along with other spiritual technologies to accommodate advanced meditative techniques like vision quests or rites of passage. Dating has also served as a method of political protest in the context of oppression of minorities (frequently religious ones; i.e. Catholic, Bobby Sands in Maize Prison was protesting for political prisoner status as a member of a sectarian minority engaged in terrorist activity).
Physiologically, the non-ordinary states are initially derived from subjects experiencing many of the side effects initially of hypo-glycemia (low blood-sugar):
Hypoglycemia causes symptoms such as hunger, shakiness, nervousness, sweating, dizziness or light-headedness, sleepiness, confusion, difficulty speaking, anxiety, weakness (NIH)
Of course, there are different formats to fasting, in/excluding water, food after sunset. However, in any situation where you alter the fuel you are feeding your metabolism, it will need to adjust to accomodate; this can cause psychological effects as well as physical.
I would caution against charging into fasting without consulting a physician as, in contradiction of whatever that online source said, fasting is not always healthy for your body. See here for a run down that lays out some of the benefits, some of the complications, and some of the controversy surrounding both.