Botulism is extremely rare in adults, is somewhat more common in infants (there are about 80 or so cases a year, while 2 or 3 cases of adult botulism per year would be about average).
The effects of the disease in infants can range from fairly mild to death, in fact, it is one of the causes suspected in sudden infant death syndrome.
Infant botulism probably happens because the kids have not yet developed the full range of intestinal bacterial fauna that in adults helps to fight off the effects of the bacterium. While contaminated honey has been identified as one source of the spores, there are many cases in which no foodborne source can be found.
The disease usually occurs in infants under six months old, and it is therefore recommended that kids under one year not be fed honey.