The yellow press (or yellow journalism) is the type of journalism which thrives on provocative headlines and sensationalism, rather than a serious presentation of well-researched news stories. The term gained currency in New York City at the turn of the 20th century when the city's newspapers were engaged in a circulation war. Alternative terms which we might use today are the 'tabloid press' or the 'gutter press'.
In the period in which Rebecca is set, one example of the yellow press would have been the News of the World newspaper. It was established in 1843 and survived until 2011, when it was closed in the wake of the phone-hacking scandal.