If what you mean is that you want to play background music through your speakers so that your microphone picks it up "in the background"... don't do that.
OBS only outputs sound to these places: 1) streaming output to a site, 2) recording output to a file, 3) monitoring device
The monitoring device is set in Settings> Audio. It should NOT be the same as your default device if you are capturing local audio from your PC (either from a game or from playing music).
If your PC is both the source of your game audio AND your background music, then no-- OBS alone cannot do this because Windows does not isolate audio this way. (I mean if your BGM is coming from a player program. You can control it independently in OBS if it is a media file source added directly to a scene).
Your game almost certainly just outputs to the default Windows audio device, and many other programs do as well. If your music player can specify a different device, then that's fine, but OBS has no control over that.
What you can do in OBS is capture each source that is NOT your default audio source separately; but if Windows puts all the audio on a single device, OBS cannot pull it apart.
For this kind of control you need software that provides additional virtual audio devices. Look at Voicemeeter: