In simple terms, a link wheel is a group of websites that use one of a few, or usually two, strategies that end up giving the punch of their link juice to a target website. Google pretty much allows this as long as the websites are not automated, spam-filled or completely irrelevant. I've seen many areas where real estate organizations employ this strategy very successfully to dominate much larger organizations on the web.
Method one: All websites point to the target website. Each spoke contributes a little more to the target site. The sites, if small, are relatively invisible. They don't show up in the SERPs for keywords and are found only if you know to search for them, or are an SEO who is assessing a competitor's back-links.
Method two: Each website in the link wheel points to the next website, lending its PR to the next site in line. The final website points its link to the target. This is a kind of Highlander strategy. Each site inherits the "life" of the site before it until all the link juice goes to "the one."
There are variations on this strategy, but that's essentially it.
Recent updates in the Google algorithms have made this strategy a little less effective, but it still works quite well with sufficient volume and good SEO practices integrated in every component.
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