I think P is different from camera to camera. My XTi P is used as basically automatic mode, except you can shoot in RAW instead of jpeg, you can turn the flash on and off, you can control the ISO, and you can change the exposure (although it decides the shutter speed and the aperture)
Well if what ChrisA describes is also true, then yes, I guess it does vary by camera. My friend, a camera user, told me that on his Canon, using P is like using AUTO, except that on AUTO, his flash would keep popping up when the camera feels that it needs to use flash. On P, it won't. You still need to control some things, but it's not like A or S where you need to control shutter or aperture.
I had assumed it was the same on my Nikon, but I'm probably wrong. I use Aperture priority all the time, and have been doing so for years. When I need flash, I pop it up myself, and when I need exposure compensation, I select that. If I'm not misunderstanding ChrisA, P mode is kind of like having Aperture and Shutter priority at the same time. If you change the Aperture, the shutter speed changes accordingly. If you change the shutter speed, the aperture changes accordingly. In A mode, if you change the Aperture, the shutter changes accordingly. However, if you try to change the shutter speed, nothing happens. You can say the same about Shutter Priority with regards to the aperture. If you try to change it, then nothing happens.