From the Apple IIe User's Guide:

The name Apple Computer was chosen late one afternoon as Steve Jobs and Steve Wozniak, Apple's founders, faced the deadline for filing a Fictitious Name Statement, part of the business licensing procedures. After volleying names back and forth with Wozniak for hours, Jobs looked at the apple he was eating and decided that, unless he or Woz arrived at something better by five o'clock, they would call the company Apple. Five o'clock came and went; Apple was the new company's name.
Interesting - considering the original logo I always thought it was a reference to Sir Issac Newton.