The Mac had already been shown off to Apple employees, analysts and the press in the fall of 1983, and the 1984 ad broadcast during the Super Bowl in January made a big public splash. But it wasn't until January 30, 1984 that Steve Jobs and other members of the Macintosh team would show the new computer to the public - specifically, a gathering of the Boston Computer Society (BCS). Harry McCracken has all the details over at Time, including a video that's worth watching.
Jobs is joined on stage by Bill Atkinson, Steve Capps and others, including Steve Wozniak, for a lengthy Q&A after his presentation. It's quite a long session - an hour and a half from start to finish.
Check out Harry's article for some context: He shares the story behind the unveiling, what it took to get Jobs and company out there, and how this rare bit of video was unearthed and pieced together. A really fascinating and unique bit of Apple history that we can all enjoy now.