PostgreSQL is a powerful enterprise-level relational database that is free and open source but also has commercial support options. It is the backbone of data repositories for many applications and web sites. Refractions Research (http://www.refractions.net) has created a product called PostGIS that extends PostgreSQL, allowing it to store several types of geographic data. The result is a robust and feature-rich database for storing and managing tabular and geographic data together. Having this ability makes PostgreSQL a spatial database, one in which the shapes of features are stored just like other tabular data.
PostgreSQL also has several native geometry data types, but according to Refractions, these aren't advanced enough for the kind of GIS data storage they needed. The PostGIS functions handle the PostGIS geometry types and not the native PostgreSQL geometry types.
This description is only part of the story. PostGIS isn't merely a geographic data storage extension. It has capabilities from other projects that allow it to manipulate geographic data directly in the database. The ability to manipulate data using simple SQL sets it ahead of many commercial alternatives that act only as proprietary data stores. Their geographic data is encoded so that only their proprietary tools can access and manipulate the data.
The more advanced PostGIS functions rely on an underlying set of libraries. These come from a Refraction project called Geometry Engine Open Source (GEOS) ...