I don't think there is an industry of hiring freelancers. A freelancer can work for any industry, and are normally hired by the company or person that had a job needing done.
There are recruiters, who find potential candidates for positions within companies (freelance/contact, temporary, or regular employee), and there are employment agencies or "temp" agencies who have a pool of employees they use to fill the same types of jobs but remain employed by the agency and not the company whose positions are being filled.
But the website you describe I think is best described as you did: a website to help companies or people find freelancers.
outsourcing
, which simply refers to the practice of contracting work that a firm might do itself to a third party. You could also describe yourself as acontractor
.