How did this practice originate and what is the meaning/purpose for it's use?
(Disclaimer: I'm going to answer this pragmatically and straightforwardly without any reference since I think it doesn't require any. There may be memorable stories about the bowl but I don't think they are really necessary to explain it. Feel free to discard the answer.)
The alms-bowl serves the purpose of helping one carry the food & prevent spoiling it with external dirt. If you went on alms-round with your hands it wouldn't be helpful for yourself or for the lay people as it would create hygiene problems. It also helps one measure the amount of food to accept, whether it's only for himself or also for others with whom he shares the food.
(As the comments below show, the next paragraph is not applicable, since monks should hide their bowls under their robes until they know someone intends to give.)
Additionally, it helps other people identify readily what the person with the bowl wants, food. In other words, if one carries a bowl around, instead of a hat or any kind of cloth, it is more straightforward what he wants. If one carries a hat or any kind of cloth, it is easier to perceive that he wants money or something else apart from food.
As for it's origin, if I wanted food I would also use a bowl. Why would I use anything else? With this I mean that the origin is not necessarily something special or traditional, it's just a pragmatic tool that anyone who wants food would use.
As I know the origin goes, before the Buddha's enlightenment. According to the legend, Siddhartha Gautama in seeking Enlightenment sat under the spreading bowers of a giant Nuga Tree lying close to the bank of river Neranjana. Then the daughter to the village chief name "Sujatha" offered a bowl filled with rice, thinking he was the divinity of the tree (You could read the full story here.
- Collect alms for one or more than one monk. For instance if another monk is too sick to go on alms rounds
- Server as a kind of suitcase, specially for the forest monks. They can keep all the robes inside the bowl and keep it away from the rain or the small animals(Insect, Mice)
- Very practical object a symbol