I believe this patent describes "Local PageRank", where 'local' means 'local to a particular search query'. Let's say that a search for "widgets" returns 1,000 results, based today's algo. Now let's pretend that those 1,000 sites represent a "mini-index", so backlinks only count from sites within the 1,000 site mini-index. So a search-query-specific (local) PageRank is calculated, and the enitre list is re-ranked.
The implication of this is that it would be really important "who" your backlinks are. If your backlinks are returned with the same search terms as your site, it will improve your ranking. This provides an incentive for seeking quality, relevant links. Links from completely irrelevant sites would be weighted lower, and so they should.