Within Judaism and other religions, fasting is conceptualized in different ways. There are three, possibly four different approaches, only one of which has biblical support.
The first approach sees fasting as a form of expiation: my bodily suffering serves as retribution for bodily sin. I experience a little bit of pain or a little bit of death, and that cleanses me from the stigma of transgression. The pre-Yom Kippur ‘Tefilah Zakah’ prayer is an excellent example of this idea within the Jewish tradition. Line after line, the prayer expresses the hope that each element of suffering purges a corresponding area of sin: not wearing leather shoes atones for when my feet ran to do evil, not eating atones for forbidden foods I consumed, and so forth. The traditional ‘BeHa”B’ fasts are in this vein as well - fasts were observed after major Jewish holidays to atone for conspicuous consumption during the holidays.
The second approach views fasting as sobering corrective. I return to spirit by denying the body. By removing the distractions of the flesh I am able to turn back to the soul and nourish it with what it requires. This is the classic Platonic view of asceticism, that the body actually impedes the soul. One need not take an extreme ascetic view in order to see fasting as a manifestation of this idea; just as easily, fasting might be an attempt to restore balance between body and spirit. It is a temporary measure to create a certain atmosphere for a brief period of time, after which things return to normal. Perhaps the mitzvah to eat on the day before Yom Kippur echoes this view that asceticism has value, yet must be tempered. In the contemporary milieu, a form of this approach is advocated by those who cast fasts as days to reflect on personal food choices.
A third possible approach was taken by R. Tzadok Ha-kohen of Lublin. He turned the equation on its head by reconceptualizing fasting not as a set of behaviors intended to effect change, but as a set of behaviors that reflect a mood. On Yom Kippur, when your life hangs in the balance, food is the last thing on your mind. How can you think about eating? On Tisha B'Av, while contemplating the smoldering ruin of God's Temple and the destruction of Jewish civilization, who even has an appetite? Who can eat?
A fourth approach is implied in Chapter 58 of Isaiah, which is tellingly recited as the Haftara on the morning of Yom Kippur. The prophet begins by criticizing those who fast and beat their chests while continuing to oppress and persecute. He declares that this is not the fast that God wants. What, then, is the fast that God wants?
At first blush, the contrast seems to fail. The "fast that God desires" is not a fast at all - it is feeding the hungry, clothing the naked, and sheltering the homeless. On further contemplation, however, an entirely different conceptualization of fasting emerges.
Is it not to...loose the fetters of wickedness, undo the bands of the yoke, let the oppressed go free, and break every yoke? Is it not to deal your bread to the hungry, and bring the homeless poor to your house? when thou see the naked, that you cover him, and that you do not ignore your own flesh? (Isa. 58:6-7)
A Jewish "fast" is more than not eating or drinking. It included wearing sackcloth and ashes as well as congregating in public places to pray and mourn (see, for example, Mishna Taanit 2:1 or Ch. 4 of the Book of Esther). Isaiah's prescription for the fast that God desires addresses precisely these elements: when you gather in the town square to call out to God, think of the people who sleep there at night because they have no home. When you feel the pangs of hunger after not eating for a day, think about those for whom this is a regular occurrence. When you don your sackcloth and ashes and take off your comfortable shoes, remember that there are those who do not have what to wear. The point of fasting is to sensitize us to those for whom such denials are a daily occurrence, and not by choice.
This approach to fasting is shared by Islam. According to Islamic law, one who cannot fast on Ramadan must instead feed the poor for a day. This link between fasting and feeding the poor is precisely the same as the one made by Isaiah.
The Jewish people, if not prophets, remain the children of the prophets (b. Pesachim 66a). Although the synagogue has replaced the public square as the site of our fasts, and although Isaiah's linkage of fasting with social welfare goes largely ignored, it is refreshing and inspiring to see that the core instinct has not completely evaporated. Over the summer, hundreds of thousands of Israelis took to the streets to protests their country's lack of social justice. Regardless of one's opinion of the protests' aims, this linkage between voluntary homelessness and sensitivity to social ills harks back to the prophecy of Isaiah.