Mainly a product of The Musical. This trope most often occurs when a composer wrote a really keen song. Or if there is a big star in the movie who must have a solo. Or the director has a favorite song that he wants to put in the movie. Unfortunately, there is really no way to inject the song into the story in the traditional "burst into song" way. So, the writer often gives us the immortal line "That reminds me of a song," or something similar and the character sits down at a piano or hops up on the stage to sing a little ditty that has....no plot significance whatsoever. ("Let's rehearse the ___ number" or "Let's film our music video" or "Let's dance to ___" and then doing exactly that are also popular.)