To be a Nielsen family means a household is part of a panelist system that is used to determine how many people watch television and in what way. It is how the TV industry gets what is known as Nielsen ratings.
These ratings are important to the television industry, as they can often make or break a show. If polled ratings are not good enough, the show could be cancelled. These ratings also effect how much advertisers are willing to pay for commercials that play during a given television show. Other details, such as show budgets and pay for the stars of the shows, depend on these ratings.