A more complete explanation can be found in this Wired News article. It explains that the early Unix engineers picked that date arbitrarily, because they needed to set a uniform date for the start of time, and New Year's Day, 1970, seemed most convenient.
You may also be interested in reading about the "2038 bug," a problem in 32-bit Unix systems similar to the Y2K bug. You can read more about the 2038 bug here.
- Answer by Amy Kucharik, Assistant Editor
This was first published in March 2005