Origins
To reveal is to pull back the veil. The word comes from Latin revēlāre — re- ('back, away') plus vēlāre ('to cover'), from vēlum ('a covering, a curtain, a sail'). The image is of a cloth being drawn aside to show what lies behind.
The Latin vēlum gives English several words. A veil is the most direct descendant. Velvet may descend from the same family — a fabric that covers softly. A ship's velum (sail) is a covering that catches the wind.
The most striking connection is with apocalypse. Greek apokalypsis means exactly what Latin revēlāre means: apo- ('away from') plus kalyptein ('to cover'). Both words describe pulling back a cover to see what is hidden. The Book of Revelation in the New Testament is called the Apocalypse in Greek — they are translations of each other.
Later History
Develop belongs to this family too, through an unexpected path. French développer meant 'to unwrap' — dé- ('un-') plus envelopper ('to wrap up'). To develop a photograph is to unwrap the image. To develop an idea is to unfold what was wrapped.
The reveal in architecture — the side surface of an opening in a wall, visible when a door swings open — preserves the physical sense most precisely. It is the part that becomes visible when the covering moves aside.