Synapse started out as an Apache Incubator project co-proposed by a number of companies. The real key starting point was a face-to-face meeting held in the Bay Area in September 2005 hosted at Infravio's offices. In that meeting the overall approach for Synapse was hammered out, and then we set out to coding.
The first real usable build followed early in January 2006. Known as M1, this was a real runnable release, but only providing very simple functionality. Other releases throughout 2006 lead to the 0.90 release in December 2006, and in December 2006, the Board voted to approve Synapse as a graduate from the Incubator and a member of the Web Services project. The namespace URL (http://ws.apache.org/ns/synapse) used in the Synapse configuration language is a remnant from our Apache Web Services heritage.
A year later, in December 2007, Synapse became an Apache top level project (TLP), and since then has released 3 versions.
Here are some more interesting resources that show the growth and development of Synapse from its humble beginnings.