The Die I used is split and held together with a grub screw, what's the deal with that. Adjustable to compensate for wear? What is its purpose and how do you use that facility in a die? More to learn for me.
Firstly, I'm only a hobby machinist, not a professional. So I'm only speaking from personal experience rather than a proper trade education in how to use these tools.
As far as I'm aware, the reason for the split in the die is to allow for some fine adjustment in the finished size of the thread. Some split dies have a built-in grub screw that opens and closes the split, something like the pinch bolt on your triple clamps. Those type you adjust the gap with an Allen key before inserting the die into the holder (or die stock). Smaller dies that don't have this built in adjusting screw are adjusted using a screw in the die stock that has a conical tip which goes into the split to force it apart, opening the gap. There should also be a grub screw in the die holder either side of the adjusting screw. Those go into dimples in the outer edge of the die either side of the split. Screwing those in will close the gap in the split die.
If you're cutting a new thread in a hard bit of bar, it can sometimes be helpful to do it in two or more passes. Open up the split as far as it will go for the first pass. It won't cut the thread to the full depth, but it'll be easier going. Close the gap for subsequent passes until the thread will fit the nut or whatever you're screwing it into. Always use a suitable cutting lubricant.
Occasionally you might want to leave threads a little oversize so you get a tighter fit than you normally find with a nut and bolt. That can be achieved by adjusting the gap in the split die. A tight thread will be a more secure fitting for something that you don't want to unscrew, like a fixed stud.
As an addendum, dies are different to die nuts. Dies are usually round and have to be fitted into a holder to enable them to be used. They may or may not have a split in them. Die nuts are hexagonal and are normally used with a spanner. They don't have splits in them. Obviously anything without a split is non-adjustable. The finished thread they produce is a fixed size.
I mostly use dies for external thread cutting (if not doing it on the lathe). I find die nuts more useful for tidying up an existing thread that may have been damaged, although you can cut a new thread with them at a pinch.
EDIT: Since posting the above, I saw someone on a YouTube video using a die stock that takes hex die nuts. So I take back what I said above about needing to use a spanner on them. What I should have said is you CAN use a spanner, but you can also buy a die stock (die handle) that will fit the hex.