PostGIS, which currently has a written version 1.5.2, is a spatial database extender for PostgreSQL Database Management System, which is used as a backend spatial database for geographic information systems (GIS), such as ESRI SDE or Oracle's Spatial extension. In contrast to the two last-mentioned database servers, PostGIS is an open source GIS software under the GNU General Public License.
If you just want to start learning PostGIS, BostonGIS has made PostGIS and PostgreSQL tutorial on its website. For starters, maybe you could start with the Getting Started With PostGIS: An almost Idiot's Guide.
There's more to learn PostGIS guidance on these sites, please look at his homepage to find other tutorials PostGIS and PostgreSQL.
BostonGIS has also released a book PostGIS in Action in hardcopy and PDF format. I've posted previously about this book in May 2009. Now the book is already a lot of revision, a more complete discussion and thicker, last updated in April 2011. PDF format of the book is actually a lot of "scattered" on the internet for download through file sharing sites. Perhaps the search with the keyword in the following url useful.