It's an arbitrary date selected in 2005 to celebrate Google's September milestones. Google first registered Google.com on September 15, 1997, and the company was incorporated on September 7, 1998. Instead of either one of those two dates, Google selected the 27th, because they're Google and they can.
It's hard to believe the search engine is now officially entering the troubled teens. I remember when Google first launched. I was enjoying a fast university internet connection and using both Alta Vista and Yahoo as my main search engines. With Google's minimal interface and lightning fast search results, I was a convert from day one. [Google]