In the automatic mode, the camera chooses EVERYTHING for you, that is:
-Exposure
-ISO setting
-Aperture
-Colour balance (vividness, sharpness, etc)
-Whether or not to use the flash.
-And a ton of other stuff.
Program mode is a lot more creative than that. It chooses the essentials, like exposure & aperture. However, it lets you choose more technical settings like ISO sensitivity, colour settings, white balance, exposure compensation, flash compensation (how powerful the flash is) and some other settings.
Some of these are avaliable through the shooting menu (accessed by pressing the "+" button on the camera), but some of them are in the Shooting Options menu (get to it by pressing "MENU", then <left>, and navigating to the camera icon).
In Program, you can also use the command dial to adjust the aperture, and the exposure will quickly get adjusted for you. (however, if the aperture is already at its maximum [lowest F number], you won't be able to do anything).
Basically, Auto is exactly that. Point 'n shoot. Program can be that, but also can allow you much more creative control over your photos.