What is actually happening to the body when you are seeing stars, that is, after you receive a bump on the head, you feel unstable, and these "stars" swim before your eyes. What the heck are they?

Something is causing the optic nerves to fire. The brain is interpreting this as points of light. Your eyeball and contents is a kind of chemical soup enclosed in a tough sac of tissue. Pressure can cause the nerves to emit electro-chemical signals. If you gently press your eyeball you will see color changes for the same reason.

Phosphene