For a monastic the bowl also represents the opportunity you give others to practice the Dhamma in accordance with their means. In Thailand, this is reflected in one of the idioms used to describe going for alms: proad sat, doing a favor for living beings. There were times on my alms round in rural Thailand when, as I walked past a tiny grass shack, someone would come running out to put rice in my bowl. Years earlier, as lay person, my reaction on seeing such a bare, tiny shack would have been to want to give monetary help to them. But now I was on the receiving end of their generosity. In my new position I may have been doing less for them in material terms than I could have done as a lay person, but at least I was giving them the opportunity to have the dignity that comes with being a donor.
For the donors, the monk's alms bowl becomes a symbol of the good they have done. On several occasions in Thailand people would tell me that they had dreamed of a monk standing before them, opening the lid to his bowl. The details would differ as to what the dreamer saw in the bowl, but in each case the interpretation of the dream was the same: the dreamer's merit was about to bear fruit in an especially positive way.
The alms round itself is also a gift that goes both ways. On the one hand, daily contact with lay donors reminds the monastics that their practice is not just an individual matter, but a concern of the entire community. They are indebted to others for the right and opportunity to practice, and should do their best to practice diligently as a way of repaying that debt. At the same time, the opportunity to walk through a village early in the morning, passing by the houses of the rich and poor, the happy and unhappy, gives plenty of opportunities to reflect on the human condition and the need to find a way out of the grinding cycle of death and rebirth.
For the donors, the alms round is a reminder that the monetary economy is not the only way to happiness. It helps to keep a society sane when there are monastics infiltrating the towns every morning, embodying an ethos very different from the dominant monetary economy. The gently subversive quality of this custom helps people to keep their values straight.
Above all, the economy of gifts symbolized by the alms bowl and the alms round allows for specialization, a division of labor, from which both sides benefit. Those who are willing can give up many of the privileges of home life and in return receive the free time, the basic support, and the communal training needed to devote themselves fully to Dhamma practice. Those who stay at home can benefit from having full-time Dhamma practitioners around on a daily basis. I have always found it ironic that the modern world honors specialization in almost every area -- even in things like running, jumping, and throwing a ball -- but not in the Dhamma, where it is denounced as "dualism," "elitism," or worse. The Buddha began the monastic order on the first day of his teaching career because he saw the benefits that come with specialization. Without it, the practice tends to become limited and diluted, negotiated into the demands of the monetary economy. The Dhamma becomes limited to what will sell and what will fit into a schedule dictated by the demands of family and job. In this sort of situation, everyone ends up poorer in things of the heart.
The fact that tangible goods run only one way in the economy of gifts means that the exchange is open to all sorts of abuses. This is why there are so many rules in the monastic code to keep the monastics from taking unfair advantage of the generosity of lay donors. There are rules against asking for donations in inappropriate circumstances, from making claims as to one's spiritual attainments, and even from covering up the good foods in one's bowl with rice, in hopes that donors will then feel inclined to provide something more substantial. Most of the rules, in fact, were instituted at the request of lay supporters or in response to their complaints. They had made their investment in the merit economy and were interested in protecting their investment. This observation applies not only to ancient India, but also to the modern-day West. On their first contact with the Sangha, most people tend to see little reason for the disciplinary rules, and regard them as quaint holdovers from ancient Indian prejudices. When, however, they come to see the rules in the context of the economy of gifts and begin to participate in that economy themselves, they also tend to become avid advocates of the rules and active protectors of "their" monastics. The arrangement may limit the freedom of the monastics in certain ways, but it means that the lay supporters take an active interest not only in what the monastic teaches, but also in how the monastic lives -- a useful safeguard to make sure that teachers walk their talk. This, again, insures that the practice remains a communal concern. As the Buddha said,

Monks, householders are very helpful to you, as they provide you with the requisites of robes, almsfood, lodgings, and medicine. And you, monks, are very helpful to householders, as you teach them the Dhamma admirable in the beginning, admirable in the middle, and admirable in the end, as you expound the holy life both in its particulars and in its essence, entirely complete, surpassingly pure. In this way the holy life is lived in mutual dependence, for the purpose of crossing over the flood, for making a right end to suffering and stress.

-- Iti 107

Periodically, throughout the history of Buddhism, the economy of gifts has broken down, usually when one side or the other gets fixated on the tangible side of the exchange and forgets the qualities of the heart that are its reason for being. And periodically it has been revived when people are sensitive to its rewards in terms of the living Dhamma. By its very nature, the economy of gifts is something of a hothouse creation that requires careful nurture and a sensitive discernment of its benefits. I find it amazing that such an economy has lasted for more than 2,600 years. It will never be more than an alternative to the dominant monetary economy, largely because its rewards are so intangible and require so much patience, trust, and discipline in order to be appreciated. Those who demand immediate return for specific services and goods will always require a monetary system. Sincere Buddhist lay people, however, have the chance to play an amphibious role, engaging in the monetary economy in order to maintain their livelihood, and contributing to the economy of gifts whenever they feel so inclined. In this way they can maintain direct contact with teachers, insuring the best possible instruction for their own practice, in an atmosphere where mutual compassion and concern are the medium of exchange; and purity of heart, the bottom line.

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