I just recently learned that the Boss TU-2 tuner can cause a significant loss in tonal quality, particularly on the highs, due it not being true bypass.

I use an Octa-Switch as my pedal board, and I've always had the tuner before the chain even goes into the Octa-Switch.

So I moved the tuner into its own switch on the board so as to keep it isolated from the rest of the chain. However this board has an On-Off Buffer button, as can be seen in the link above.

Could somebody explain to me what exactly this will do in regards to my fx chain, pedals, etc? Can I simply have the tuner in any switch, and if I toggle the buffer to On it will eliminate that problem?

Putting the tuner in the loop removes it from the chain, so no worries about its crap buffer. The Tu-2 buffer won't be in the signal chain ever if you just keep it on and have it in the loop.

You're just replacing the on/off from the TU-2 with the on/off from your octaswitch. So just choose whichever buffer/TBP mode you want from the octaswitch and enjoy. Usually you'd want to buffer just the first switch and then have the buffer off on the rest of them. You might even find that you don't need the buffer at all. The goal is to have as few buffers as possible. If you need one it should be quality and as early in the chain as possible.

Short answer: Tuner in the 1st loop, buffer on there unless it sounds better without it.