In earlier centuries the drinking water in many towns and cities was of poor quality and drinking it could lead to disease. Many of these places also knew the fine art of brewing, and thus the worthy citizens would brew a lighter bodied, lower alcohol beer that could be drunk at any time of day. Traditional beer is unfiltered, thus containing yeast, which prevented the growth of pathogens. The hops in beer are a natural antibiotic, and the small level of alcohol would also play its part in safegaurding the drinker's health. Some small beer would also be flavoured with fruit in a similar way to Belgium's Lambic.

Note: J. Totale's writeup is technically correct, but misleading, as it suggests that the term "small beer" refers to a drink made without hops and consumed only by children. People have been brewing in order to allow safer consumption of water since long before the English discovered the use of hops, as is documented in the legend of Saint Arnold. Historically beer brewed without hops was known as "ale" and brewed with hops as "beer", and, according to Kevin Trayner, small beer (also known as table beer) was consumed by adults and children alike.
Actually, before the fifteenth century beer was brewed without hops, and so was brewed often. Everyone drank very strong beer with their meals, and even the children drank beer. However, the children weren't given the same beer as the adults, but instead had a 'small beer', which was less alcoholic - Which is where the saying comes from, similar to child's play.

The irony is of course, that even the small beer consumed by the kids was more alcoholic than full strength (around 5%) beer today.

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