Reducing the CPU load to render colours and do gamma correction must save some power.
Less memory and fewer refresh cycles on the screen must also save some power too.

Traditional colour LCDs have a uniform white backlight, then pass the light through red, green and blue filters, then through LCD to let through a variable amount of each colour. This results in a display that is about 6 times less efficient than necessary.
If you made a greyscale screen by dropping the RGB filters, you could get away with 1/3 of the power to the backlight. (just using the LCD in on/off mode to produce a black and white display would halve the power again.) However, I see that greyscale is only used in power-save mode, and at other times it still has full-colour. So this can't be the method...

(do correct me if i am wrong) This only happens in LCD displays (pretty much any phone apart from most Samsungs), not AMOLED screens, like Samsung Galaxy series.