Aperture Priority mode focuses the controls of the camera around aperture, as the name states. It allows you to adjust aperture, and will automatically adjust the shutter speed based on aperture. Aperture priority is good when you want a certain depth of field.

Shutter priority mode is just like Aperture mode, but reversed. You can adjust the shutter speed and the aperture will automatically adjust to your setting. Shutter priority is good for sports events or capturing moving images.

Manual mode gives you full control of the settings. You adjust the aperture and shutter speed however you want on your own, giving you a wider range of exposure.