Source music refers to music in a drama (e.g., film or video game) that is part of the fictional setting and so, presumably, is heard by the characters. It cannot be background music (e.g., from a radio or TV), but can be produced by characters themselves as part of the plot.
The opposite of source music is underscoring, which is music heard by the viewer (or player), intended to comment on or highlight the action, but is not to be understood as part of the "reality" of the fictional setting.
Source music was sometimes used as scores from the earliest days of Hollywood talkies, in some cases — e.g., The Public Enemy (1931) and American Graffiti (1973) — using it to the exclusion of any underscoring; or in Touch of Evil (1958), where there is proportionately more source compared to underscore.