The overlapping consists in advancing (or extending) the sound of a scene into the other. It is used to make a semantic link between two scenes, and in particular, the action of the anticipated music is a consequence of the first scene.
Usually only the music of the second scene is anticipated, while the diegetic sound of the first scene continues. This procedure can create a confusion in the audience who needs to reprocess the information.

Long overlapping linking scenes

Music anticipation to link scenes in Yakushiji Ryōko no Kaiki Jikenbo, cap.9

Music anticipation to link scenes in Boardwalk Empire 2×04. Analysis by Antonio Sarió Balada

Short overlapping creating semantic links

El anticipo del sonido para crear un encabalgado genera un enlace narrativo, generalmente la escena de donde emana el sonido «influye» en la escena donde se ha superpuesto el sonido encabalgado.

Music anticipation as narrative link in The Journeyman, cap. 1

Music anticipation as narrative link in Boardwalk Empire 2×01 (Analysis by Javier Sánchez-Moreno Giner). In this case, the music from the rich and powerful (Debussy’s ‘Clair de lune’) interrupts the sound of the poor and powerless, «shutting up» their diegesis.

Music overlaying in Grimm 2×06. In this case there is not a clear semantic link and it becomes a mannerism that may confuse the audience.