I shoot in RAW when the resulting photo matters i.e. when the photo is for publishing and I shoot in JPG when it's just something like holiday snaps.
As Kipax has said, the RAW image is all the data the camera stores when it takes a photo. From that you can adjust things like the exposure, white balance, contrast, saturation to fine tune to elements you got wrong when you pressed the shutter.
Basically shooting RAW is like shooting with a film camera and playing with a RAW in Photoshop is like sticking your negative in a darkroom for developing.