A virus is an idea, bit of code, or unit of information that requires a host to reproduce itself. Viruses can infect a life form, computer system, or culture, with various effects. Some viruses simply reproduce themselves, while others can have a payload. A meme is a cultural virus, while the life-form originating the term is simply a piece of coded DNA or RNA 'software' wrapped in some sort of protective shell. Many viruses can cause sickness, damage, or other deleterious effects on the host, but some can be manipulated or specially crafted to have specific beneficial effects.
A worm is a special type of virus that can reproduce and transmit itself directly from host to host.