Google Custom Search Engines let anyone create a search engine with results based on Google's index, with an added layer of human editorial selection. Put more simply, you create a Google CSE; you select the sites you want in it, and then you let anyone search your CSE from your site. New Google CSEs appear almost daily. You can see examples at Google here, and there's even a directory of them being maintained here. Google CSEs offer a couple link building opportunities, one of which might be described as affinity linking.
What is affinity linking and how do Google CSEs impact it? As always, it best to illustrate by example. How's this for verticality (no pun intended): Soaring Search. This search engine is oriented towards glider pilots, students, and instructors. This search engine gives higher rankings on glider-related results than other similar sky sports such as hang glider, para glider, RC glider, etc.
The first link building opportunity is to look for Google CSEs in your niche. If you run the Soaring Society of America site, then it's a pretty good bet the folks over at Soaring Search will have an affinity for your content and include your site if they haven't already. Have they? Yes. But that's an easy one. The Soaring Society of America is a non profit association-type site. Of course the folks at Soaring Search have heard of it and included it.