I see that a lot of fluid websites use a min-width and max-width property on their web pages designed mainly for desktop. When the browser width is less than min-width, content stops shrinking and the user has to scroll horizontally. I can relate to the rationele behind it. As far as I understand, it basically means that the content is designed so that shrinking its width past this point will make it unusable. It is acceptable, because that page is designed with a minimum width in mind.
But I cannot fully understand the use of max-width property on the main content. These websites usually limit the growth of the content container and center it. Why not let it fill the screen since you are already using percentages instead of pixel values? Web sites like Outlook or Gmail fill the screen whereas a lot like Amazon choose to limit the width and center the content.
Edit: Great answers so far and I would like to add one other point: Some sites (e.g. Google, Amazon) extend the header infinitely when limiting the content area width and some others (e.g. StackExchange, StackOverflow) choose to limit and center "header content" but extend "header background" infinitely. I also wonder your comments on the significance of this in terms of UX.