What do you mean, young master's appetite keeps you sharp?

It means picky eaters. Being picky about food means that you like to eat, not most things, but only your favorite food, so young master's appetite makes you picky about food. It shows that the young master's appetite makes you used to eating and picky about food. Young master is a general term for the disciples of rich families in the old society, and it is the name of the son of a prominent family.