Centroid, or central point of relevance, is a central reference point of an area as determined by a search engine.
Today the centroid for Google searches is most heavily based on the location of the searcher.
In the past it was based on the geographic centre of the city. That meant businesses closer to the city centre had a competitive advantage. Then the centroid moved more towards the largest cluster of a business category in an area. Most recently, there’s been a weighting towards the physical location of the user.
This evolution has significantly reduced their importance for local search.