pgRouting is a powerful extension for Postgres that provides geospatial routing functionality, allowing users to calculate the shortest path and perform network analysis on graph-based structures. It can be used in Geographic Information Systems (GIS) for tasks like determining the fastest route between two locations, as well as in non-GIS applications such as task scheduling, resource allocation, and recommendation engines. pgRouting implements Dijkstra's algorithm and A* algorithm to find the shortest path between nodes in a graph, making it an efficient solution for various use cases. It can be used on Supabase and has a wide range of applications, including finding critical paths in project schedules, optimizing data transfer between servers, and building recommendation engines like YouTube's.