What is the reason behind fasting (vrat)?
One reason for fasting is to atone for one's papa (usually translated as sin).
For example, in Mahabharata Santi Parva, section 36, Vyasa said,
By penances, religious rites, and gifts, O Bharata, a man may wash off his sins if he does not commit them again. By subsisting upon only one meal a day, that procured by mendicancy, by doing all his acts himself (without relying on the aid of a servant)....by becoming a brahmacharin and always ready for exertion, by casting off all malice, by sleeping on bare ground, by publishing his offence to the world, by doing all this for full 12 years, a person can cleanse himself from the sin of having slain a Brahmana. .....By living upon the scantiest meal every day for a space of six years, a person may be cleansed of that sin . By observing a harder vow with regard to food one may be cleansed in three years . By living upon one meal a month, one may be cleansed in course of only a year. By observing again an absolute fast, one may be cleansed within a very short time.
REF: Ganguli's translation of Mahabharata, Santi Parva, Section 36
 Ganguli remarks in a foot note that the rule laid down is that he should eat in the morning for the first three days, in the evening for the second three days, eat nothing but what is got without soliciting for the next three days and fast altogether for the three days that follow.
 The harder rule referred to is eating in the morning for seven days; in the evening for the next seven days; eating what is got without soliciting for the next seven days; and fasting altogether for the next seven days.
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