Spot Metering

Your camera is equipped with a light meter that can read exposure values all over the scene you're shooting, and for the most part,your camera uses these readings to give you very reliable exposure settings so you can get the exposure you want.  There are four main types of metering modes that you can choose from:

1. Matrix/Evaluative Metering.  The default metering mode for any camera is usually called matrix or evaluative metering.  This mode takes exposure readings from throughout the frame and averages them together to give you an exposure reading that gives roughly equal value to every part of the frame.
2. Spot Metering.  Spot metering takes all of exposure values from the center of the frame.  The center "spot" usually covers about 2 or 3 percent of the frame.
3. Partial Metering.  Partial metering is very similar to spot metering, but the "spot" is larger, covering around 10% of the frame.  Some cameras may have partial metering with no spot metering, and some may have both.
4. Center-Weighted Metering.  Center-weighted metering takes exposure values throughout the frame, but gives more weight to readings the closer they are to the center of the frame.  

Of these four metering modes, I only use the first two.  I use matrix metering over 90% of the time and use intuition to set exposure compensation when needed.  I also frequently check my photographs in the camera to see if my exposures are accurate.  

But spot metering is very useful when there is one part of your image that you need to have properly exposed.  When you use this mode, you are basically telling the camera that you would like to expose for the center of the frame and let the exposure for the rest of the scene be set relative to the center of the frame.  Here are some examples where spot metering can be extremely helpful:

1. Sunrise/Sunset.  In sunrise and sunset or sunset pictures you do not want to overexpose the sky.  To ensure this, you can zoom into the scene and put the brightest part of the sky without the sun in the center of the frame.  If your camera is set to spot metering, you can use exposure compensation to chose a value +1 to +1-1/2 stops above the light meter reading.  Then zoom back out, recompose and shoot.  Your image will display the sun (if in the frame) as a white disc, but the sky will display color and detail.  Objects in the foreground may turn dark or even black, but the earlier you take the sunrise picture, the less this will be a problem.  Many of the best sunrise/sunset photos are taken just before sunrise or just after sunset. 
2. Light/Dark subjects.  If you're shooting a very light or very dark subject, you usually want to retain detail in the subject.  Suppose you want to take a picture of a Great Egret--a bird with all white feathers.  You can zoom into the brightest part of the egrets feathers, and set your exposure compensation to about +2 stops (the value will vary based on how the bird is lit).  Then zoom back out, recompose and shoot.
3. Portraits.  If shooting portraits outdoors, you want the skin tones of your subject in the image to match their skin tones in reality.  If the scene around you has a lot of contrast, matrix metering may give you images where your subject is over or underexposed.  You can zoom into your subject and set your exposure to the proper value for the skin tone of your subject.  Then zoom out, recompose and shoot.

This method will work as I've described above only when your shooting mode is set to Manual.  If you are shooting in any other mode (including Av/A or Tv/S), your exposure values will change when you zoom back out and recompose after spot metering.  Now your camera has an "exposure lock" button that will freeze your exposure settings for about 30 seconds while you recompose and shoot.  But if you take too long, you'll lose your exposure settings, and if you want to take another shot, you'll need to go through the whole process again.    This to me makes no sense; it makes a simple task difficult and complicated.  The easiest way to shoot while spot metering is to shoot in manual mode.  In manual mode, the values you set when you zoom in on your subject will remain the same until you change them, so you will only need to go through the process of setting your exposure when the lighting of your scene changes.

For the above image, I set my camera to spot meter in manual mode.  Then I zoomed into the brightest part of the sky without the sun in the frame.  I set my exposure to +1-1/3 stops.  Then I zoomed out, recomposed and shot a bunch of photographs.