Exposure compensation - the beginner question

What is exposure compensation actually doing and why is it needed?

I am new to phorography but as far as I had understood there are 3 ways to increase the amount of light captured by the sensor:

• Open the aperture as wide as posible (limited by your lens and acceptable DOF)

• Longer exposure (limited of how steady the camera or object is)

• Higher ISO sensitivity (limited by the capability of your sensor and image processing)

An then exposure compensation can also affect the amount of light captured, but does it slightly increase/decrease the exposure, or does it fiddle with the ISO or something else?

If it slightly changes one of the above why is it needed at all just to make things more complicated? Couldn't there have been an exposure fine tuining (e.g. 1/250 could be slightly pushed to 1/265, etc) or fine tuning of the ISO, etc ? rather than keep track of an extra factor?