GH offers free hosting so lots of people use it.
I use S3 instead of GH pages as I am a control freak.
if you run Jekyl locally it will compile the site into a folder named
_site, you can take that and do anything you want with it - ftp it to your own server, put it on S3 etc.
The slick thing about GH is that you can just have all your source files in version control using Git and the free GH service, and GH will run jekyll on the source files anytime there is a commit and compile a site for you and serve it all automagically… so for lots of things it is a great combination. I do use this for one of my sites - a personal blog of sorts and I end up doing everything on GH and it sort of ends up being a little like a CMS in that I can do it all from the online interface. For my real sites for my business I do everything local and then push the site folder to S3.
PS I came from using DNN CMS for 10 years or so - Jekyll is so much better for my use case, and I don’t have to worry about unpatched code or something leaving the server vulnerable. CMS’s have their place I suppose, but for a lot of/most sites a static generator is better in my opinion.