To be continued is in the passive voice and shortened from: The film is to be continued. The infinitive is often used in headlines to indicate future action. In 1972 it was announced that President Nixon of the USA was going to pay a visit to China. I remember this newspaper headline: Nixon to visit China.
Many TV shows consist of two parts. The first part will stop at a place in the story where there is high suspense. You are very excited and really want to know what happens next.
Instead, they put in big letters "to be continued..."
It means that the story will continue next week. You have to wait a week to see how the story