A contrived example to clarify further: Let's say that there is a link, foo.gov/taxes_in_retirement. Locations with a high concentration of retirees might click on the link more frequently compared to other locations. In privacy mode, from this location, a search for "taxes" might rank that link higher in results based on this activity (even though the search didn't contain the word "retirement"). This shows how a link might be ranked differently depending on search location even if the link itself is not inherently location-specific (as oppressed to, say, a local-news link).
Also, search engines can play with inconsistent ranking of results to see how click-throughs might be affected. For example, if moving a link from first to third in the result list has no effect (people continue clicking on the same link even though it's now third instead of first), then it's a pretty strong signal that the link should continue to be ranked first in future results. This experimentation of search results is even more important the more uncommon a search is because there is less confidence in the current ranking until there is more activity to base the ranking on.
Just as stores shift around product placement (front of the store, back of the store, etc), a search engine is free to shift around search results. Keep in mind that product producers might pay for better in-store product placement too, just as customers pay search engines for ad placement in search results.