Short answer: FEC (flash exposure compensation) applies an offset to the flash output power calculated by the camera for a "correct exposure of the subject". FEC does not influence aperture, shutter time and sensibility (ISO) settings.
The working principle of flash photography with Canon is roughly as follows:
aperture, shutter time and sensibility (ISO) are set based on the ambient light (measured when you press the shutter half-way).
flash power is set to correct the exposure of the subject (subject = whatever is behind the focused AF-points, correct exposure = 18% gray).
That said, if flash light is the dominant light source for the subject (e.g. low ambient light or subject in shadows) and ambient light ist the dominant light source for the background (i.e. the background is so far that it gets few of the flash light used to lift the subject) then:
exposure compensation regulates the exposure of the background (apply a negative/positive value to render the background darker / brighter)
flash exposure compensation regulates the exposure of the subject (apply a negative / positive value to render the subject darker / brighter)
exposure compensation and flash exposure compensation can be therefore used to regulate the contrast between background and subject.
Sure there is a lot more to know about that (E-TTL working principle, influence of shooting modes and metering systems, auto-fill reduction, etc). For more details I recommend you to browse the following links:
John Seymour wrote:
(Flash compensation) Is this supposed to
1. Change the balance between flash and incident light (attempting to keep the overall exposure 'correct' by metring with the new higher/lower flash output),
2. A more simple increase/decrease in flash output with the camera setting the overall exposure as if there were no compansation?
With Canon there is nothing like an "overall exposure" to be "corrected" or "set as there was no compensation". There is ambient light (set by aperture, shutter time and ISO) and there is flash light (set by the flash output power). Flash complements ambient light in the achievement of optimal subject exposure.