Headway Themes is best described as a wordpress theme framework that gives it’s users the ability to create websites with little to no knowledge of programming. It allows non-web professionals to immediately setup a website in a few minutes while giving them the a multitude of options for customizing it. Think of it like using WSYWYG software for building your website.
Headway Themes framework gives the user an easy to follow dashboard that removes the confusion on what would otherwise be a complicated method of creating, editing or updating your wordpress website. The Headway Themes introduction video explains it best below: