Exposure compensation adjusts the exposure up or down as much as you ask it to do. Depending on the mode and the ISO setting (manual or auto) it will adjust the 'floating' variable up and down. If you're in Tv mode and you set the shutter to 1/60th and it suggests f/4 and you suggest -1/3 exposure compensation it may adjust the aperture to f/4.5. If you suggest +1/3 it will likely adjust the aperture to f/3.5. It isn't "messing with" things, it is doing what you asked it to, it is adjusting the settings to where it would have metered if it had metered higher or lower as you've set in exposure compensation.
If auto ISO is set then it might adjust that rather than the aperture. In Av mode it will bump the shutter speed, leaving your selected aperture. In P mode it will adjust the program up or down, adjusting one or both of aperture and shutter speed and ISO if set to auto.
It is really for cases where you think the meter is wrong. The meter is expecting 18% grey so if you are metering white snow or a black tuxedo it will be 'fooled' so you'll want to adjust the exposure. Same for backlighting.
You can adjust the exposure later in post processing but it is best to get it right in camera if possible. Exposure compensation or manual mode can help you do this rather than just trusting the camera's meter.