Most websites in the internet have a fixed width and only a small part is using the full width of the browser. This is mostly due to the fact that there exit so many different screen resolutions including the ones of mobile phones and other devices that it is hard to fit the content nicely into all of them. A fixed resolution has an additional advantage: The site looks more or less the same regardless the screen resolution or size of the screen. It is thus more recognizable. From late 2012 things might change though, because a new trend towards “responsive” layouts is spreading. A responsive website changes its appearance depending on the screen size, making best use of the available width at any time. If the screen is very small, large images are automatically resized, content is being redistributed more vertical than horizontal and text size can also vary. There are many promising approaches to this, in particular with WordPress themes.
However, right now, most sites have a fixed width, which is usually not wider than something close to 1000 pixel in order to display well on screens with a resolution of 1024×768 pixels, which is still a common resolution despite the fact that modern screens ususally offer much more.
Therefore there will be some areas on the screen that are not covered by content and that is where your background would show up. This background can either be blank, you can choose a colour, a background image, background image animations and sometimes you even see advertisements. If you don’t want the background to be plain white and you do not want a background image either, as it might distract from the content of your site, you can use a background pattern. Patterns as backgrounds of websites are almost as old as the internet itself. I used them in the late years of the past millenium and there are thousands of them available in the web, or you can easily create one yourself. However, the is the website SUBTLE PATTERNS where there are available hundreds of very well made patterns under a Creative Commons Attribution-ShareAlike 3.0 Unported License. You can testdrive them directly on the website and download them without any need to register. Whether you use exactly the patterns you find or you take them as a base to create your own ones, SUBTLE PATTERN is a great site with clean, modern and very well designed backgrounds.