RGB curves allow to apply a curve adjustment individually to each of the RGB channels. This provides a fine control over image color balance when curves applied to each of the RGB channels are different. Using RGB curves one could make warmer highlights or colder shadows, simulate film cross-processing effect, etc.
The purpose of Luminosity Mode in the RGB Curves tool is to alter image luminosity by changing the contribution of the RGB channels to it, while keeping image color the same.
The effect is somewhat similar to V changes in the HSV Equalizer, but is smoother and broader across hues, not as selective. When working on black-and-white images, similar adjustments could be made via the Channel Mixer, but RGB Curves allow a finer control.