It is just a little perk. the newest pokemon games lets you customise a bit more your character choosing hair and eye colour on top of your sex. Later on you find some shops where you can spend your battling money buying clothes, hats and haircuts in addition to the usual pokemon survival things. To be honest I haven't progressed enough in the game, so I am stuck with an earlier change of luck I did with my character. I kinda want to start over but I don't want to lose my pokemon.
I like the second image the best.