To show an example, I just now went outside (bright sunlight) and took these photos. In each case, the photo on the right is taken with Spot metering, and the left photo was taken with center-weighted averaging. No other camera settings were changed between photos. Open an image by clicking on it, and use your right and left arrows on your keyboard to switch between the photos.
Notice on the left ones, the lighting is more washed out. On the right-side photos, the subject stands out much better against the background. This is hopefully a good demonstration of the power of spot metering.