The Nielsens (named after the Nielsen ratings) are a family of fictional characters from a 1950s sitcom that's been canceled; they've been relocated to the real world, which is different from the world they know. They use a device called a Turnerizer (named after Ted Turner) to switch between color and black-and-white within their home. Mike Duff, the teenage son of the family next door, is the only real-world person who knows their secret.
In most episodes, there are guest appearances by actors from classic TV shows, playing their characters; e.g., Gale Gordon appears in episode 1 as Theodore J. Mooney (from The Lucy Show).