This is a very broad question - the use of 'empty' space either side of the main site wrapper varies from site to site, depending on the function or purpose of the website. Also, depending on how the site is constructed (e.g. is it responsive?) it could potentially be a lot of work to make the site margins work the way you want them to, or point the user to the content that you want.
I've built several websites with large photographic backgrounds (utilising handy CSS scaling methods like background-size: cover; - love that rule!) to fill the space or communicate brand values, such as colour palettes; these can be very attractive and are a lot less monotonous than using flat colours, but often impact on loading times.
I've seen a lot of sites (e.g. http://www.pcgamer.com/uk/ ) that utilise in-margin advertising to fill the perceived 'empty' space in the site margins - depending on what kind of site you're building (e.g. e-commerce), this could be appropriate or useful, but they can be irritating for the user if they accidentally click on an advert when trying to click something else, so like most other considerations there is a UX decision to be made in using this method.
I hope these examples help - I guess I would advise not to make your margins too distracting, or to make them overly purposeful. IMO a bit of empty or 'dead' space can really help a design to breathe.