A website sponsorship can benefit both parties. If you've recruited a sponsor for your site, you can use the funds to pay the designers, programmers, hosting fee and any staff you have hired. The company that sponsors your site will have its name displayed in a prominent position on your site, giving people the opportunity to see the business' name. Some people may feel that because the business is supporting a community site, for example, that they should support that business.
If you've successfully recruited a website sponsor, you will have to come to an agreement about how your sponsorship will work. Likely, the sponsor will pay you a set fee on a monthly or annual basis, and you will be able to renegotiate that fee at the end of a set period, such as a year. If your site is increasing in popularity and success, you will likely seek more money from the sponsor. The sponsor may wish to remain if your site statistics show that your readership is increasing -- and you may even have other businesses approach you, seeking to sponsor your site. If this is the case, you may be able to have multiple sponsors for your site.