Sphinx is a full-text search engine, distributed under GPL version 2. Commercial license is also available for embedded use.
Generally, it's a standalone search engine, meant to provide fast, size-efficient and relevant fulltext search functions to other applications. Sphinx was specially designed to integrate well with SQL databases and scripting languages. Currently built-in data sources support fetching data either via direct connection to MySQL or PostgreSQL, or using XML pipe mechanism (a pipe to indexer in special XML-based format which Sphinx recognizes).
As for the name, Sphinx is an acronym which is officially decoded as SQL Phrase Index. Yes, I know about CMU's Sphinx project.