Example. I have a category called (and I'm leaving out the brackets because..pretend they are there) Category:XXX Occupashun, Someplace. Oops, look, that is misspelled and it has 8 profiles attached, and there's a big old explanation of the category in the text. DO I feel like going to each one and editing the category? Heck no, I have better things to do. So, I find the right category, and it's Category:XXX Occupation, Someplace. So I can {{Rename Category|XXX Occupation, Someplace}} and when EditBot runs the next time, it will be all set. Now, if Category:XXX Occupation does not already exist, I can still do the rename function; however, the page, after you save it, will have a red link in it to the new category, which must then be set up. If you don't set up the red category, EditBot will have a hissy fit when it runs, and the process for this rename stops until a Categorization project member sets up the new category. So, just copy over the parents and the text on the category page to the new one and save it. EditBot will run, rename the category, and delete Category:XXX Occupashun, Someplace.
If Category:XXX Occupashun, Someplace has 52 members, we can still do the rename, but it will have to be confirmed by a Cat Member with such abilities (there are 4 or 5 of us, I can't recall exactly). Then EditBot runs with it.
I could also merge by using {{Merge Category|XXX Occupation, Someplace}}. Same thing applies. New category must be set up BEFORE EditBot runs, or EditBot will spit it out and a categorization member will have to set up the new category. All of the old data in the category edit box will be copied over to the category it is merged into, so, later on, it will have to be cleaned up. The Bot leaves a trail something like
<!--Bot Merge blah blah
the stuff from the old category
End bot Merge-->
Something like that, I don't have an example right now as the Category:Merged Categories is empty.
What slows down your rename or merge? Not having the new category set up with parent categories...having more than 10 profiles attached to the category...anything that requires a manual intervention. It will add at least an extra day to the process.