Worms are often lumped in with viruses and your antivirus software should stop either one, but they're not the same thing.
A virus gets its name because it embeds itself into your operating system or another program, then replicates itself and uses your PC or your server to carry out its function, which is usually the destruction of one or more files. But unless it attaches itself to an email, it stays only on the host computer.

A worm is much nastier. It is also a computer program that makes copies of itself, but it spreads from computer to computer (instead of file to file), infecting whole systems, using up resources in the affected computer, and because of that, they're much harder to stop. Worms can get into your computer's memory from a network, find network addresses of other computers, then send their own copies to these addresses. So, worms are designed to spread, while viruses generally stay put. Worms take over your computer while viruses destroy files.