The equal time rule is a rule that says that broadcast TV stations must give free time to all candidates in a race if they give free time to any candidate in the race. There are many exceptions to the rule, however.
The point of this rule is to prevent a network from favoring one candidate over another. The networks are supposed to be unbiased at least in this regard. They cannot give free advertising to one candidate and not to another. An example of this was when Arnold Schwarzenegger ran for governor of California. When he ran, the networks stopped showing movies in which he had appeared since that would have constituted free time being given to him. The same was true when a man named Fred Thompson, who had been an actor on the show Law and Order, ran for president in 2008. During the time that he was still a candidate, NBC did not rerun his shows.
The implication of this is that the networks have a responsibility to be fair to all candidates. They are not allowed to favor one over the other. This means that they are said to have some sort of civic responsibility that other businesses do not have.