Well, a few things to clear up. There is only one thing that effects your exposure, and that is the amount of light in the scene, your aperture, and your shutter speed. Since we can't always control the light, we can adjust shutter speed(which may lead to motion blur) or we can adjust aperture(which effects our depth of field). Now, we can also use ISO, which amplifies the signal that our sensor recieves which does introduce noise. Those are all choices we have in manual.
Exposure compensation doesn't work in manual. In automated modes, it will bias the meter to make it think a subject needs more or less exposure, which means:
in program mode, it may change aperture, shutter speed, or ISO
In shutter priority, it will change aperture if it can based one lens limitations
In aperture priority, it will change shutter speed possibly leading to motion blur.
If auto-ISO is enabled, it will generally change the shutter speed until it hits a low limit that you set and then start raising ISO.
In general, exposure compensation simply tells the camera meter to behave as if the scene was metered lower or higher than it actually reads it and the mode you are in determines how it reacts.
I don't use it very often since I rarely shoot outside of manual.
Now, flash exposure compensation is completely different and I use it quite often. It will influence the TTL metering from the flash to put out more or less power. Very handy and quick to adjust for changing conditions.