What does "Exposure Compensation" do?
If your camera-produced JPEG are coming out darker or lighter than you like, then you can use "Exposure Compensation" to make the JPEGs lighter or darker.
If you select one stop of positive exposure compensation, the resulting JPEGs should be one stop lighter. Similarly, a stop of negative exposure compensation should make the resulting JPEG one stop darker.
Image lightness is a result of the relationship between exposure (light reaching the sensor) and the ISO setting. The camera's metering system strives to find an exposure that will give a reasonable result in the context of the selected ISO. Depending on the selected mode, the camera may try to alter aperture, shutter speed, or ISO to get a good match between the exposure and ISO.
Conceptually, Exposure Compensation applies a bias to the camera's metering system.
When you select a positive exposure compensation, you bias the meter to think there is a little less light. This will cause the camera to try for a higher exposure and/or a higher ISO.
The name "Exposure Compensation" is a holdover from the days of film. With film, the camera could not adjust the film speed, and therefore the only option available to the camera was to try to raise the exposure.
With digital cameras, it really should be called something like "Lightness Compensation," as it may alter ISO instead of altering exposure.