A bookworm can be any sort of creature which likes to eat books (or, more specifically, the materials that books are made of). The most common one is the booklouse, which likes to eat the mould that grows on badly maintained books, and cockroaches and silverfish will also eat these as well as happily chewing through fabric bindings and starch pastes used to keep old books together. Woodworms will also eat through paper, although usually only to get to wood on the other side.
Modern books tend to be safe from bookworms as their bindings aren't quite as tasty, but the best way to stop any book damage is to make sure you keep your books somewhere warm and dry. Yes, that means you need to stop leaving them in your bathroom- and definitely no more reading in the bath!