Most people viewing a Twitter page see a blank column either side of the main tweet area. How wide these columns are depends on the screen resolution being used.
You can make your own Twitter background and take advantage of this space. If you have a business (or personal) website, you might like to design a custom Twitter background to match your own website.
Designing Your Own Custom Twitter Background{+}
I use the free Paint.net software, but you can design your background in any graphics software.
There are a lot of illustrations in this guide, so rather than reproduce it here I have turned it into a downloadable pdf file.
You are welcome to download it for FREE.