What does amber mean on a mood ring?

Nothing, really. "Mood" rings show a color that roughly corresponds with the heat coming from your finger and they can't measure your mood at all.

To demonstrate this, take your ring off and put it in a refrigerator for a few moments. It will turn dark. They hold it against a cup of hot coffee. It turns light. Mood rings have a chemical in them that changes color according to the ambient temperature, just like those forehead fever thermometers you can buy at dollar stores.