Why do Bollywood films stop for songs?

Because in Indian popular cinema a song is not a break from the story: scholars describe it as one of the ways the story is told. Songs express emotions that dialogue might struggle to convey, and they are often used to advance the plot. A typical Indian film may feature five or six choreographed songs.

Here is the difference with Hollywood. Hollywood musicals often took the world of entertainment itself as their plot, so characters sing because they are performers. Indian filmmakers used song and music as a natural way to express a given situation, and there is a strong Indian tradition of narrating mythology, history and fairy stories through song and dance. Song-and-dance in Indian film began when sound arrived: the first Indian sound film was Alam Ara (1931).

Behind this is a different idea of what a story is for. Writing about the masala genre, Tejaswini Ganti says that its central premise is that viewers derive pleasure from being taken through a series of moods or emotional states. In contrast, emotional tension in Western film is generated with plots, following Aristotle's Poetics. A masala film, named after a mixture of spices, blends action, comedy, romance and drama.

A note on words: 'Bollywood' refers only to Hindi-language films, though it is often used mistakenly for all of Indian cinema.