After forty days on Sinai, Moses came down with the two tablets of testimony in his hand, and something had happened to his face. The Torah's Hebrew says karan — literally, his face had "horned" or "radiated." Targum Pseudo-Jonathan on Exodus 34:29 decodes it: the visage of Moses' face shone with the splendour which had come upon him from the brightness of the glory of the Lord's Shekinah in the time of His speaking with him.
This is one of the most striking details in the entire Torah, and the Targum highlights the stranger half of it: Moses knew not. He walked down the mountain glowing, and he did not realize he was glowing. He only discovered it when Aaron and the elders flinched from him (Exodus 34:30, in the next verse).
The rabbis drew a moral from Moses' obliviousness: the greatest sign of true holiness is that its bearer is unaware of it. A person who knows they are radiant is already dimmer for the knowing. Moses had spent forty days so close to the divine speech that its afterglow clung to his skin, and his mind was still back in the cloud, still hearing the words, not attending to himself.
The Targum's expansion — the brightness of the glory of the Lord's Shekinah — chains four words together (brightness, glory, Shekhinah) to emphasize that what Moses carried down was not a metaphor. It was a reflection of the divine Presence, a borrowed light, soaking into the prophet like scent into cloth.
The takeaway: proximity to holiness marks a person. Moses' shining face is the Torah's way of saying that what you spend your time near — that is what eventually lights you up.