Both a virus and worm are types of malware programs that range from very annoying to extremely dangerous.  Viruses attach themselves to programs or files, and count on humans to run the program or open the file in order to infect a PC.  Worms, a subset of computer viruses, are similar to viruses but they do not require any human action to infect a PC and spread throughout a network and even beyond, say by emailing itself to everyone in your address book.  (To learn how you protect yourself, see, How do I prevent spyware and malware?)