By 1980 the AE-1 was beginning to show its age. The competition had caught up or beat it on features, so Canon decided to update it. Rather than call it the AE-2 or something reasonable, they decided to go with the more confusing AE-1 Program, and styled it so that it looked almost identical to an AE-1. The problem, of course, was that it was real hard to see why you should pay for the program when you could still buy a perfectly good AE-1 for a lot less.
The obvious addition was a program mode, which is Canonese for fully automatic. Most cameras from the 70s had a priority mode, where the photographer would set the aperture (called aperture priority) and the camera set the shutter speed, or the photographer set the shutter speed (called shutter priority) and the camera set the aperture. Cameras had one mode but not the other. Most Canons at this time were shutter-priority. Most Nikons and Minoltas were aperture priority. The program mode was full-auto: the camera picked both. Seems stupidly simple in hindsight, but it's more complicated than you may think. The camera can't just pick a combo, it has to pick an intelligent combo, and that requires some more computing horsepower. And this is 1980, when the Apple II still ruled the desktop world, and cameras had computers the size of a fingernail. There wasn't a whole lot they could do.
The real payoff for buying the AE-1 Program was the accessories. In addition to the full line of FD lenses and all the stuff you could hang on an AE-1, you could also attach a faster autowinder, the super-fast motor drive that (up to this point) could only run on the A-1, and you had user-interchangable viewfinder screens. Even the A-1 needed to be sent to the shop if you wanted to change screens.
I think this a great camera. I used to put the motor-drive on it and take it out and it worked great; it had all the good things about the AE-1 plus a little bit more.
For more information: Canon Camera Museum
Modern Photography magazine camera test: August 1981
Modern Photography magazine "SLR Notebook" camera preview: June 1981
One of Modern Photography magazine's Top Cameras
Camera manual: Orphan Cameras.com