Worm
A worm is an animal that usually lives in dirt or else inside other animals. It also describes a type of computer infection that is deliberately placed in a computer but does not actively destroy the computer (although it can be used associated with a virus to cause major destruction or to harm other computers). A computer worm can also be used to distribute spam.
The worm animal is small and wriggly, is hard to catch, and in some cases if it is chopped in 2 it turns into 2 different worms - the tail end growing a new brain and wriggling off!
Inside another animal's body, the worm slowly and steadily breeds, eats away at the other animal's body, and slowly destroys it. Depending on the type of worm, they can do anything from forcing the animal to eat more than normal through to causing minor irritation right through to death of the host. In some cases, however, the worm is actually beneficial to its host, getting rid of nasty bacteria and infections in a symbiotic relationship.
A computer worm is named after the animal, in that they are almost impossible to find, in some cases if you catch them they turn into 2 new worms, and they slowly but steadily breed.
The computer worm is usually sent with something fairly innocent. If you get a worm on your computer, it is very difficult to detect it. Your computer doesn't do anything any differently, except that it might work slightly slower, but not by so much that you would notice. Unlike a trojan horse, the worm does not secretly activate later. The worm itself does nothing.
The purpose of the worm is twofold: 1) To replicate itself and send itself on to other computers and 2) To aid in something else which is nasty. The second element can be the spread of a virus or sending spam everywhere or a variety of other things.