Exposure compensation exists because there are certain subject/lighting scenarios that would fool the camera meter in to giving an incorrect exposure if left to it's own devices. Typical examples are either very dark subjects or very bright subjects. If you take a snow scene as an example, the camera meter doesn't know that it's looking at a snow scene and just measures the amount of light coming through the lens and sets the exposure accordingly. The result is an underexposed image because the camera doesn't recognise that all the additinal light is because the subject is a very bright subject rather than a street scene under a fierce mid day sun.
In that situation, if shooting in one of the auto modes, you could use EC to dial in an additional extra stop or so, thus telling the camera to meter the scene but then add a stop to the settings that it calculates based on those readings.
In manual mode, the camera isn't making any decisions with regard to what aperture or shutter speed to set, you are. That's why it's called manual mode, but it's also why EC doesn't work in manual, because the camera isn't in charge of any settings that it can change to make the compensation. If you need to make some sort of compensation while shooting in manual mode, just change the ISO/aperture/shutter manually.
