What particularly is Jonas self-conscious about?

Jonas is self-conscious about his blue eyes.

Now, he was reminded that the light eyes were not only a rarity but gave the one who had them a certain look — what was it? Depth, he decided; as if one were looking into the clear water of the river, down to the bottom, where things might lurk which hadn’t been discovered yet. He felt self-conscious, realizing that he, too, had that look.