The tradition to abstain from food for a day or more has existed since Old Testament times. All Jews were required to fast before some important events, battles or in times of calamities. Moses himself was fasting on Mt. Sinai.
The annual worship calendar of the Orthodox Church marks several days when the faithful are required to abstain from food all day long. These days include Holy Friday, Exaltation of the Cross, Christmas Eve, and Theophany Eve. There is a tradition in Greece not to eat anything during the first three days of the Great Lent, that is, prior to the first Lenten Liturgy of the Presanctified Gifts. Many Greek Orthodox believers observe that rule.
However, most people may find this level of abstinence too demanding. That is why the Church has never adopted this pious custom as a requirement for all believers. The Orthodox Church emphasizes the quality of fasting, not its length or strictness. Abstinence from food is an essential part of fasting but not the only one. The Orthodox attitude to the fast is holistic. It includes not just denial of certain foods but also abstinence from bad actions and ill intentions. With that said, if someone feels eager and strong enough to abstain from food during the whole day, one can do so with the blessing of his or her spiritual father.
Translated by The Catalog of Good Deeds