Sometimes identified as just “P”, Program mode is a great way to experiment with various shutter speed and aperture combinations. Each combination produces what the camera calculates to be a “correct” exposure based on the available light and other factors.
Once you select Program mode, you use one of the command dials to scroll through the combinations and then select the one that will best capture what you are trying to achieve. For example, if you want to freeze the action, select a combination with a fast shutter speed (i.e., high number, e.g., 500) and the camera will choose the aperture.
Similarly, if you want a shallow depth of field to make the subject stand out from the background, select a combination with a wide aperture (i.e., small number, e.g., 3.5) and let the camera choose a shutter speed that will produce a good exposure.
Note that you may also need to select your ISO setting (assuming your camera enables this for this mode) based on the available light, e.g., 100-200 if you’re outdoors on a sunny day, or 400 and up if it’s cloudy, or even higher in low-light situations.
Program mode is particularly useful when you want to easily capture a number of different types of exposures - some where the shutter speed is most important, and others where you want to control depth of field. I use it when I'm wandering around without knowing exactly what I'm looking for :).