When you choose Av or Tv mode you are imposing a specific value to your camera. In Av mode (aperture priority) you decide what aperture value you want to use then your camera will automatically give you a speed value resulting in a "correct" exposure. This is why it's called Aperture Priority!
In Tv (time value or shutter speed) mode, you decide to set shutter speed and then your camera gives you an aperture value.
Exposure correction/compensation modifies the value computed by your camera
while leaving aperture (in Av) or shutter speed (in Tv) as you set it.
what situations you would use it?
Generally, you use compensation for difficult or complex subjects such as snow, white sands, lava beds, heavy backlit situations. This is true for scene that are not middle-toned.
In other words when you feel that your camera meter will be fooled.
Other situations are when you want to have a personal spin to your photos. Sometimes you want to under-expose to get darker photos and more deeply saturated colors.
Michael has an excellent tutorial about exposure.
By the way, use slides to experiment.
Hope this helps - write back if it doesn't.