The term viral video refers to video clip content which gains widespread popularity through the process of Internet sharing, typically through email or IM messages, blogs and other media sharing websites. Viral videos are often humorous in nature and may range from televised comedy sketches such as Saturday Night Live's Lazy Sunday to unintentionally released amateur video clips like Star Wars kid, the Numa Numa song, The Dancing Cadet, and The Evolution of Dance.
As I understand it, that refers to a video clip that is extremely popular. Hundreds of thousands of people view it and send its URL address to their friends, and so knowledge of the video spreads a bit like a virus spreads. It does NOT mean that the video is any type of virus.