Drizzle came into being for both social and technical reasons.
The Drizzle project began in 2008 when Brian Aker forked it from MySQL, following Sun Microsystems' acquisition of MySQL. The Drizzle project was announced in 2008 at the O'Reilly OSCOn Open Source Conference.
In terms of technical goals, Drizzle is based on a micro-kernel design that aims to be as pluggable as possible. Anyone should be able to quickly extend the database for their database needs. Drizzle has been designed for modern architectures and deployments. Drizzle does not shy away from breaking with the past, many of the MySQL "Gotchas" (features that work as advertised but not necessarily as expected) have been removed.
Drizzle is open source software, designed in an organic manner by developers that span different companies. The development process has been geared to be more similar to the Linux Kernel where no single company owns the source code, or provides all of the developers. In stark difference to MySQL, the goal is to be as inclusive as possible and provide stable releases. The social charter of Drizzle encourages diversity and prizes respectful dialogue between all participating parties.
Drizzle today is the most active fork of the MySQL server. At the time of writing, core developers span five companies, with as many, and sometimes more then, 30+ developers participating each month. Drizzle provides releases every other week and is the most well-tested database in the MySQL family tree.
More narrative on the project can be found on Wikipedia