Diegetic sound has a clear source that can be seen on screen. 

Nondiegetic sound has no visible source on screen. 

Filmmakers use this distinction when featuring music in their films. 

In this clip from Fellini's Amarcord, the barber plays a flute and thus the sound of the flute is heard on the soundtrack. It comes across more realistic as what is heard has a source on screen. 

This scene from Herzog's Fitzcarraldo shows Fitzcarraldo sitting on a log while an aria plays in the background. This would be nondiegetic music as there is no visual source for it. It's more commonly used in film.