Average takes the overall reflected light from the center of the frame with a gradual falloff towards the borders. Basically akin to autoflash, but through the lens so focal length doesn't play a role.
Evaluative puts more emphasis on the area around the active AF point. How that is affected by focus and recompose is...predictably random.
And then we have the II, which incorporates distance information to avoid mishaps from image content that deviates to much from a neutral gray subject. At least while the flash is on camera and locked straight forward. Can cause surprises when used with an off camera cord.