The way it works is that each class gets its own subset of four skills. Whenever you change to that class, you get those four skills. However, if you unlock a skill by leveling up high enough, you can equip it in the active skills list. The star icons indicate skill slots that will work regardless of your form. So, here, you could pick "Bully" from the Low-Level Goon's skills, and if you were to put it in a starred spot, you could then use Bully regardless of your transformation. Non-starred spots are only active when you're in Jimmy's normal form.
I probably should have taken a screenshot of a lower-leveled character so I could show that equippable skills are level-locked, but I seem to have ironically made the Low-Level Goon rather high leveled.