Hi Tony;
For the first couple of years that I had the Taig lathe, I didn't have a mill, and made everything with just the lathe and milling attachment. I have a mill now, so some of the projects on my pages are done only with the lathe, and some with both the lathe and a Taig mill.
A dividing head will let you divide a circle into a given number of portions. For instance, if you want to make gears, it will turn the gear blank to the individual positions of each tooth one at a time.
You can do a lot of the same work with an indexing plate mounted to some sort of spindle. The amount of spaces the indexing plate can divide a circle is limited to how many index holes the plate has.
Boring stuff follows, but may give an idea how the dividing head works.
The dividing head divides by use of a worm gear. The ratio of the worm to the gear tells you how many divisions you can get per full rotation of the worm. A crank handle is attached to the worm gear to rotate it. So, if you have a 60:1 worm gear in your dividing head, then for each revolution of the crank handle you get 6 degrees of a circle. That in itself will divide a circle into 60 perfect parts. If you put an index disc on the end of the shaft that has 60 holes in it, you can use the holes to index to finer divisions. In the case of a 60:1 dividing head with a 60 hole index plate you can divide a circle into 3600 individual equally spaced parts. Very handy for doing things besides gears, too. If you need to make a bolt hole pattern in a piece of material with something like 16 holes, you would have a hard time laying them out by hand. Very easy to do with a dividing head, though, and for some numbers easy to do with a simple indexer, too.