The skills are used to improve different jobs and activities in the game. They are not needed to get scenes.
Charisma is used to earn more money from working as a waiter.
Knowledge is used to earn more money as a cook.
Fitness can be used on fishing.
Sublety can be used on bets.
Appearance can improve chances for tips.
You can use stats for other things too such as finding out info about the girls or learning lore from artifacts in the museum.