A computer virus is a program that is designed to duplicate and spread itself in any form without knowing it exists. Computer viruses can also attach themselves to a file. Viruses can also infect documents such as created in word document.
Worms are very similar to viruses but are technically different from the virus in the way the spread trough out the computer system. It needs to be extract or run to activate the spreading of worms and can be dangerous when it runs to the computer.
How does it infect a computer system? Computer virus insert itself into a file or executable program. While, worms it exploits a weakness in an application or operating system by duplicating itself.
In the end worms are considered more dangerous because of their ability to spread and duplicate rapidly through a network. And a virus harms individually an PC and so its damage is more localized.
Freedom of Coding: He May Be a Black Hat, White Hat or a Phreaker 