"Don't feed honey to babies" is one of those things-you-ought-to-know rules (like "don't mix ammonia with chlorine" and "don't use beach sand when making concrete") that needs more publicity because it is so important.
The word botulism describes a type of poisoning. A strain of bacteria called Clostridium botulinum creates a protein called botulin, and this protein is the cause of botulism. Botulin invades excitatory nerve cells where they meet with muscle fibers and blocks the junction so no signals can get through. The result is paralysis, and in severe cases it totally immobilizes and can kill the patient.
Botulism bacteria are common in nature, but they are killed by oxygen. Therefore, the bacteria form spores that protect them from oxygen, and these spores activate once they get into oxygen-free environments. The most common way to get botulism is from improperly canned food. Once the can is sealed, it creates an oxygen-free environment. The can is then heated, and if heated properly the spores die. If the can is not heated properly, however, the spores activate in the sealed can and fill it with toxin. Because botulin is a protein, heating will destroy it. But if the canned food is eaten cold, botulism occurs.
Babies get botulism from honey in a different way. Bees naturally collect botulism spores as they are collecting nectar and mix them into the honey. Most people can eat these spores without difficulty because we have bacteria in our intestines and robust immune systems that eliminate the spores. Infants do not yet have these defenses. So when a baby eats honey, the spores find themselves in the oxygen-free intestine and come to life. They produce the toxin while inside the baby.