Using a mix-minus
As the name implies, a 'mix-minus' is a full mix of the various audio sources being recorded or broadcast but with your - or a guest's - microphone excluded.
They are used to prevent echoes or feedback from being heard as someone is speaking.
For example, if someone were to record a voice track or take part in a live phone-in without a mix-minus being used, they may hear their own voice back on a slight delay, which can be distracting.
Some audio interfaces - like mixing desks or external sound cards - have built-in mix-minus options which can be used. This is sometimes referred to as a 'clean feed'.
Check your audio device's documentation for help setting up and using a mix-minus.