What is 3 Way Linking?
Some webmasters own multiple sites and try to build up one of their specific sites by offering link exchanges from their other sites. In doing this they add a link to you on their other site and get you to link to the main site they are trying to build up.

What Benefits Exist in 3 Way Linking?
Citation analysis works well in academic environments but kinda falls a part in a commercially driven direct marketing environment (which is what the web is).

Many search algorithms may be able to detect link trading as an artificial means of boosting the popularity of both sites and discount the value of these links.

By doing a three way link from sites hosted on different servers a webmaster can build link popularity without the search engine being able to detect the link trading as easily.

The Problem with 3 Way Link Exchanges

Most people engaging in 3 way link exchanges are doing it with the express intent to manipulate search results. This typically means they are trying to make automated bots think their ideas are better than they are, and are willing to do deceptive things to do it.

The real problem is that if their two sites are not connected and they are primarily working to benefit the link popularity of their main site then it does not really hurt them if the site linking to you gets banned. If those sites get banned then they parse no link popularity to you.

In doing this webmasters can agressively market their high margin websites while keeping them somewhat shielded from the dangerous effects of their aggressive promotion.

In fact many marketers might set up 20 or 30 or more secondary sites to exchange links with.