Albert Barnes Commentary Exodus 34:33-35

"And when Moses had done speaking with them, he put a veil on his face. But when Moses went in before Jehovah to speak with him, he took the veil off, until he came out; and he came out, and spake unto the children of Israel that which he was commanded. And the children of Israel saw the face of Moses, that the skin of Moses` face shone: and Moses put the veil upon his face again, until he went in to speak with him." — Exodus 34:33-35 (ASV)

Paul refers to this passage as showing the glory of the law, though it was only a ministration of condemnation and was to be abolished, to enhance the glory of the gospel, the ministration of the spirit, which is not concealed by any veil from the eyes of believers and will last forever (2 Corinthians 3:7–15).

Regarding Exodus 34:33: the word 'when' should be supplied, rather than 'until.' Moses did not wear the veil when he was speaking to the people, but when he was silent .

Moses went in (Exodus 34:34)—that is, to the tent of meeting.