Just what the topic implies. I have green eyes what does that necessarily mean?

It means that you have the genes for green eyes.

It means both your parents carried a recessive gene that you were lucky enough to get.

Nothing. It is a recessive trait. Brown eyes are a
Dominant trait. It just means one series of genes is more likely to be passed down genetically.

They have nothing to with actual emotional traits. Unless it is Anime. Anime tends to use eye color and hair color as a way of giving off percirved personality traits.

I have magical color changing eyes.

They can be green, a bluish grey, and blue. Maybe hazel also, but I don't think so.