Quick set means you have a stem and crown that pulls out with more than two positions, and it is used to quickly correct the date or day, and in some watches, other functions as well. The reason this must be done correctly is that failure to observe the procedure will damage your watch.
Quickset began to be used in the Fifties, and various methods were patented to attempt to avoid the 'round and round' syndrome which used to be necessary to set a date on a watch that had stopped from disuse. This applied to both Automatic and Manual wind of course, so depending on the power reserve of the watch, you would pick it up after a couple days sitting on your desk or dresser, and in addition to setting the time, the date (if it had one) was also incorrect.
The first thing you need to do is determine what time it really is on the watch. Rotate the hands forward to 12 O'Clock and see if the date flips over. If it does not, keep going to the next 12. If the date flips, that means midnight. If it still doesn't, the mechanism may be broken or there could be other issues. What is important is that you now know where midnight is. In the older watches with no quick set, you now have to advance to midnight to get the date to advance, then backup to around 8:30 or 9 and forward again to midnight, advancing the date each time until the correct number shows. This old system is the back-and-forth one and caused extra wear to the Cannon Pinion. It was an improvement over the even older method which I mentioned, the 'round and round', which meant you had to go forward a full 24 hours to advance the date.
Makes it pretty tedious, I can tell ya.
So fast forward to the modern era and quick set. Different companies adopted the quick set at different times, so you might be surprised that your 1978 Rolex is NOT a quick set, but your 1968 Mido is. In addition to this, different companies experimented with different mechanisms, and some were just weird, and didn't last. Examples are the 'push-pull', and a mid seventies Omega device that set the Day by rotating the hands backward. Every couple mins would roll a new day past, which makes setting the watch back more than a couple mins a bit challenging, because you will automatically be rolling the Day as well.
But back to the procedure.
So you pick up the watch, you advance the hands, you know where midnight is. Anytime after say 2am and before 8pm, it will be safe (In ALMOST all cases) to use the quick set. In most modern watches, this is the middle crown position. There is all the way in, middle, and all the way out. All the way out is the hands setting position we all know.
So you pull the crown halfway and now you can set the date and day, depending on your model. Now you advance the hands to whatever time it actually is, and Robert's your Uncle's Brother.
So what's the big deal anyway, you ask?
If you try and use the quick set during the hours that the watch is already beginning to change the day or date, you can strip the teeth off wheels in the motion works, and your watch is now damaged and won't work properly. Other parts may break, depending on the design of the mechanism. What is really important though, is that this can also apply to quick setting Quartz watches.
So let's say you pick up your watch and the battery is dead, no problem, you change the battery yourself. (Or you take it to a trained professional, but if you do it yourself, use finger cots. Do NOT touch the battery with bare fingers, or the inside of the watch anywhere) And of course you use a quality battery, not some cheapo bulk purchase no name abomination.
Now you want to set the watch, and all the above protocol applies. The quick set mechanism can be damaged in exactly the same way as those mechanical watches. This doesn't happen as much with quartz watches, because the batteries last a year or more, so you aren't picking up a dead watch that often.
So that's it. A very important tip to avoid damaging your precious timepiece, and we do see a lot of watches that have issues from this sort of thing.
Keep on Tickin'.