JavaScript doesn't process the actual data to the database....that's done with server-side scripting - PHP.
You install the php files on your web server. When the user fill sin the form, and clicks "submit" the request is processed by the PHP scripts. For all the functions involved, there are literally hundreds of PHP files, all working together, to make it work. It's not a case of a few JavaScript files; far more complicated than that.
The ideas is to host Machform on one site, and then embed the forms in any site you like - without the need to actually install Machform on every website. (you can do that, but requires domain-specific license - e.g.. the normal version, you get one installation of Machform, but embed as many forms as you want to various sites - all the form processing is done by Machform itself.
I hope that kind of answers the question, otherwise, I think you're seeking a very technical and in-depth explanation, outside the scope of this user forum.