Traditional Linking
In a traditional tracking solution, links provided to your partners (AffiliateSite.com) point to the ROIAdvantage server, where the requisite tracking data (highlighted in red) is captured before the visitor is forwarded on to your domain (YourSite.com). So the traffic flows like this:

The visitor is instantaneously redirected to your site, but the link still points to ROIA. This is a perfectly functional solution for a great many marketing programs. For those that want to reinforce their brand recognition and for who search engine result ranking is a high priority, Direct Linking offers a very cost-effective solution.
Direct Linking
In a Direct Linking model, traffic flows uninterrupted from a partner's website to your domain, by clicking a link to yoursite.com with tracking information appended at the end. Once the visitor arrives, a special, invisible code captures the tracking information and forwards it to ROIAdvantage, while the visitor remains at your site the entire time. In this case, the flow of traffic is:

Clean Linking
Clean Linking technology allows publishers to promote your site with a basic link to YourSite.com, with no tracking parameters in the link, and still be appropriately tracked. In a clean linking scenario, your publisher registers the domain or domains where they will place your tracking links, for example, AffiliateSite.com. Once you approve them, the ROIA system will track any click originating from that site as a publisher referral to YourSite.com, again using an invisible piece of code installed on your page, which forwards tracking information to the ROIA server.

The major benefits to Clean Linking are:
Clean links do have limitations, the main one being that Clean Links must originate from a registered domain. While certainly a powerful & useful utility, they will not function in an e-mail marketing scenario (in this case, consider Direct Linking), or if the special Page Tracking Code is not present on the target page.
Why it matters
Google and other major search engines use complex algorithms to determine the order in which sites appear when a given term is searched for. One of the major factors in this algorithm is how many other sites link to yours. In traditional tracking, those links point to our servers, which while very effective, do not help your search engine rankings.
In Direct Linking, you have affiliate links pointing at your domain, which counts toward this search engine popularity. There are still tracking parameters present in the link, which many believe still prevents you from receiving full credit for the incoming link.
Clean Linking maximizes the benefit your partnership program brings to your business. Not only do your affiliates refer you traffic, which increases your sales, but you also gain the full advantage of all those additional links from sites with related content pointing directly to your site, which increases your search engine ranking and drives even more traffic to your site!