Somewhere in the middle of the movie, where Mia and Sebastian where about to kiss in the cinema, the movie that they were watching suddenly stopped.
But why did the movie suddenly stop?
The film melted on the projector. This happened from time to time when physical film was used during projection in a movie theater. Because Mia and Sebastian were watching a classic film at a (presumably) old theater (remember that it's closed down later in the movie), it was being shown on an older film projector rather than being projected digitally.
This occurrence also plays into what comes next in the plot; the "fictional" scene in the movie was no longer needed to bring them together, so it could melt away and allow them to re-create their own emotional connection, driving to the Griffith observatory themselves and sharing their dance in the planetarium. This play between what's "real life" and what's so fragile in a screen projection (which we, as audience, would be experiencing when watching this movie in a theater) is one of the major themes we draw from the movie.