I can think of two ways to achieve this effect.
The first way is to use an <iframe> that includes a 'name' attribute so your links can specify it as a target in the <a>nchor tags. This is the easiest method, but it requires that the content to be displayed is a complete webpage.
But if the point of all this is to keep the user on the same page for everything the website will contain, I'd strongly advise you against the idea if for no other reason than it becomes very difficult to manage. It also makes it difficult to impossible for the search engines to discover your content. So if that was your plan, you'd be much better off with a more conventional site structure. If you just want to have a page within your site that has changeable content, then this approach can work. Good luck!