If we could place “things” (like web pages, or simple answers to questions) on a map (like the world map), where the location would be basically their “meaning” (what the post calls “points in the conceptual space”).. then two things with the same meaning would be closer to eachother.. like two neighboring countries.
The closer two “things” are, the more relevant they are (conceptually closer).

So the idea here is to place “things” on a “map” where “distances” can be measures.

The tricky thing here is defining a “map” with its rules and measurements that actually have any coherent meaning to base the claim that “closer” means something real.