They determine what your tamagotchi will turn into, what job they will be able to do, and etc.
You can earn them by playing games, eating certain foods, going to school/work.. This is for the V4.
To determine your tamagotchi skill points go to the First Icon (Meter) press B and you should see the happy and hunger icon, press the B two more times and you should see the skill points.
Pencil Icon (Intelligence points)
Star Icon (Arts/Fashion points)
Flower Icon (Social/Kindess points)
Also you can take a look at this V4 Growth Chart Here.To see which tamagotchi needs to be high in which, so they can turn into a certain character.