Imagine a typical workplace. Suppose your company offers IT related services to their clients. Your company will have a sales workforce that shall go scouting for new clients. They will explain the background, past projects, etc. to every potential client in order to find projects. Once a project is secured, the development team takes care of getting the project done. 

Now, what if you can find projects for yourself and do things? This is what freelancers do. They basically find job of their own (with no job commitment but with or without other contractual commitments with the client) and do work. Freelancer websites are those that help these freelancers meet their prospective clients, communicate to them their expertise and get business. 

Finding the best freelancer website depends on what your domain of expertise is. Are you the one with an inclination towards literature and writing? Or are you a hardcore programmer? Or are you a detective? Every profession could have agencies providing freelance jobs. 

On the internet, it is easier to find freelancer websites that are for those who are looking for website-related work; be it web development or Search Engine optimization or web content writing. Some of the popular websites in this domain are Getafreelancer, RentACoder and Elance.

If you are a writer looking for websites offering purely writing jobs, then websites like Suite101 and Demand Studios should offer the right job. Please note that some websites might not work with people from certain countries. So it is always better to confirm about the availability of their service in your country before applying. 

For other domains, you may Google for the related keywords or you may post it on Yahoo Answers. There are always tons of sites ready to serve your purpose. Happy freelancing!