That is an analogue audio cable for ODD. Actually it has a long story. In the past (about 15~20 years ago), the reason of using that cable was not just to save CPU power. At that time, that was the only way to play an audio CD using an ODD! The sound was coming through this analogue cable and then a PC sound card just passed it to speakers, just like line-in inputs.
It may sound odd for you, but it's true. The technology to directly extract digital data from a CD to PC via ODD and the data cable was invented & adopted later. Say, today, it is very natural to extract CD tracks to WAV files (or mp3, wma, ..) with no problem, but at that old time, only a few of ODDs supported digital Audio CD extraction and usually they were more expensive. Isn't it interesting? I actually owned a CD-ROM drive which did not support digital audio extraction and I must connect that cable between the ODD and my Sound Blaster to listen to the music. This means, I couldn't rip my audio CD digitally!
In the meantime, there was another tricky case. The ODDs started having the "direct CD audio extraction", but some of PC games at that time were on mixed-mode CDs which contain both of program data and CD audio tracks for BGM. This means, the ODD should be able to read data whilst playing audio tracks, and some ODDs did not support this way with "CD audio extraction" mode. So the analogue mode was still useful. However this limitation went away so quick that almost nobody remember this sort of nasty problem actually happened in the past.
Anyway, it's just a fairy story now, and it's almost pointless to use that cable and the connectors today. All modern ODDs are able to digitally extract audio tracks and modern PCs don't have any problem to play them on-the-fly. They just still keep this analogue connectivity for no reason. Probably it's disappearing - recently, I checked some ODDs for laptops and they didn't have the connector at all.
Perhaps, this cable is still useful when you're going to reuse your old ODD as a standalone CD-player, especially if the ODD does not have front phone jack. However, this may be still pointless anyway because most ODDs today don't have a play button at front panel. There might be another usage to get another analogue line input on your PC sound card as you can easily tweak one end of that cable to conventional stereo audio jack but.. there are inexpensive audio cards now to get multiple analogue line inputs for recording.
In conclusion, I believe that you may just get rid of it and forget about it as I failed to come up with a good idea to reuse this cable, except for telling a fairy story! :)