Simply put, proximity to searcher is the closeness of the searcher's address to the point of search. In Google, the results would appear in the Google Maps results, and the business results would be sorted by proximity to the searcher's physical location. This Searcher-to-Business Distance answers one question primary question: Which businesses are closest to the searcher?
Proximity to the searcher is more accurate on mobile devices because the searcher's location is more accurate with GPS data. On desktop and wifi devices the location is a bit less accurate because it relies on IP addresses. This means that the search results will vary between mobile and desktop.
In many cases, people may be looking for the closest commodity product/service such as fuel for their vehicle. If you are low on gas finding the closest gas station can be beneficial. The cost of gas is fairly standardized amongst competitors and most stations offer self-service for convenience. This is where the proximity to searcher is extremely beneficial.
On the other hand, if you are looking for highly specialized products/service it is not the best factor. Let's say you have a serious tax problem and want to find the most reputable tax accountant in the city. If you are willing to get the most experienced business accountant to help you avoid penalties and interest with the CRA, then driving 30 minutes to his/her office is no problem.
With proximity to search, your results may not be ideal in this case!
Using Google search, you may have to try multiple search queries or find another source altogether to find exactly what you are looking for. In this case, the proximity to searcher factor is not the strongest indicator.
Proximity to search moves us in the right direction for a mobile-first world. We should expect to see improvements and updates in the future to improve search results.