It is audio output from the device to be connected to other equipment. Commonly color coded as White = Left channel and RED = Right channel.
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If I understand the question, you are trying to intertwine different functions. Like your ears, the audio input jack receives an audio source, while the audio output jack transmits outputs audio content - similar to your mouth. If you are trying to redirect the input audio directly to the audio output port you will need a "passthru" (aka monitor) function. -P2E
An audio summator is, in essence, the mixer. It takes various source inputs and "summs them up" into one audio output (to drive the speakers, for example).
Assuming you are connected to the audio output connectors on the TV, you might have to turn up the volume of the TV to get any audio to appear at the output connectors. If it is a high end set, go into the audio menu and switch the audio output to FIXED. This will give you full level audio at the connectors and then turn down the sound from the TV speakers. Don't use the internal speakers when using the sound system.
Digital audio stream
If your tv has an audio output you can connect it to the aux input of most Bose wave systems.