What causes an old truck to run better when you boost the octane of fuel; also...is it possible to put too much Octane, and destroy engine?

A lot of possible causes, but one would be:  the engine of the "old truck"  (make,year,mileage,condition unknown) could have accumulated a lot of carbon deposits over the years . . . . which can actually increase the compression ratio . . . which would respond well to higher octane gas.  It probably was not designed for high octane - and it would benefit from a complete, old-fashioned tune-up:  new spark plugs, points (if it has them), timing adjustment, carb adjustment (if it has one), filters . . .  it might be to the point of needing a valve job.

First, please identify your "old" truck. 

Second, please identify the octane booster.

I can only tell you that higher compression engines prefer higher octane gas.  By higher compression, I am talking about nothing crazy, in the neighborhood of 10;1 & up.  Around 11:1 they ABSOLUTELY have to run on high octane gas, & 92 is not high enough.  You said that it was an "old" truck, but you did not say how old.  In the "old" days, the early '70s & '60s, they made horse power with compression.  If your "old" truck is of that vintage, or someone put higher compression pistons in it, this could be the reason.  I have an old Jap 4 cylinder that was somewhere in the neighborhood of 11:1 & it ran shltty on 94, but when I could find 100 low lead (airplane gas, aka av-gas) it literally purred. 

Your EXPECTATION, and the placebo effect.

On the other hand, what you incorrectly called octane booster could have cleaned the fuel injectors, but had nothing to do with octane.

Gas that sits will lose some of its volatiles, adding an octane booster mitigates that situation and reduces pre-detonation (ping). That was done way back in the day by adding tetraethyl lead into the fuel, but that was bad for the environment so other methods were introduced like early computer-controlled advance mated to knock sensors. Since you didn't state the year of the truck something you need to be aware of is the lead served as a "lubricant" for the valve and seats also, and without lead or a lead substitute you can hammer the seats into older heads that weren't heat treated specifically for dealing with that. 

Octane does not offer any better fuel mileage, increase engine horsepower, or make the engine start quicker. Higher octane only reduces the likelihood of engine knock or ping. ... Because higher octane gas burns slower, it is more resistant to knock when subjected to higher RPM and cylinder pressures

Bort is f-ing clueless.

A) Because higher octane burns faster and runs cleaner.  

B) An engine will run on anything that will combust. The issue with using alternative or very high octane fuels is that, yes, they can 'blow it up' because of what I shared as an answer to question A and similar reasons along those lines. 

It can warp or even break important internal parts of an engine running extremely high octane in an engine that isn't built with internal parts that can handle high octane. 

An older cast big block engine should be able to handle high octane, an aluminum block? You're pushing your luck. Aluminum is a lot softer than cast steel or iron and has a much lower temperature threshold so aluminum damages and warps or breaks much more easily than a cast block. 

The octane probably wasn't and still isn't the real cause of it running poorly. When was the last time it had a tune up (spark plugs, coil packs (or distributor cap and coil if it has those), spark plug wires, oil change, MAF sensor cleaned or replaced, O2 sensors checked and replaced if they need to be)? 

All of those things as well as other parts could be the cause. Running higher octane might help for now but it will probably only be a temporary fix. It's surely not just the fuel octane that's making it run poorly.  

Have an auto parts store do a diagnostics test on it if it has an OBD port. They do that for free. If it's older than 1996 it doesn't have OBD and in that case give'r a tune up. 

The first thing I would do is check and adjust the timing of the engine if it needs adjusted. New spark plugs and wires at least if not the whole kit including the distributor cap and coil or coil packs. That's where I would start attempting to correct it permanently on an older engine that doesn't have a way to run codes and know exactly what the cause is. 

If you are not mechanically inclined and know how to do those things it's best to have a shop check the timing and do the tune up. Timing could also be why it's not running right and higher octane seems to make it run better.