The impetus for setting it up was actually several-fold. The primary reason was that developers had no one to speak for them in the USA Congressional debates of early 1994. The publishers had the IDSA, the developers had no one. People in the game industry wanted to join something, and there was nothing to join. It became very clear that a true professional society was needed to give developers a voice.
Another reason was simply that a professional society to advance the state of the art, and do all the things that a professional association does, was overdue. The community needed a way to share experience and work together on issues on an ongoing basis.
The CGDA came into being just as the old, previously privately owned, Computer Game Developers Conference was being sold to Miller Freeman (now CMP). Miller Freeman and the CGDA continued to collaborate on the conference, and Miller Freeman provided initial support for the CGDA.
In 1999, the CGDA was having a tough time with mainly volunteer labor to run the organization. The board of directors turned to Miller Freeman to contract them for management services. Around the same time, the CGDA changed its name to the International Game Developers Association to better reflect its growing global scope and platform agnosticism.
The IGDA continued to contract with CMP for day-to-day operation/management services until the end of 2004. As of January 1st, 2005, the IGDA ended the management agreement with CMP and have been directly running the day-to-day operations of the association under the wise governance of the elected board of directors.
(Note, this is a very brief/partial history of the IGDA. We're working on a more fleshed version...)
The Escapist covered the IGDA backstory in an article titled "Let's Get Together", written by Erin Hoffman on October 2nd, 2007.