In the West, masks are mostly worn for protection, think of dust masks, ski masks, or surgical masks. But sometimes masks are worn to hide the identity of the wearer. Consider this definition of mask from Encyclopedia Britannica .
Mask, a form of disguise or concealment usually worn over or in front of the face to hide the identity of a person and by its own features to establish another being. This essential characteristic of hiding and revealing personalities or moods is common to all masks.
Masks generally are worn with a costume, often so extensive that it entirely covers the body and obscures the wearer’s recognizable features. Fundamentally the costume completes the new identity represented by the mask.
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Origin Of Masks
|African Tribal Masks|
The mask, therefore, most often functions as a means of contact with various spirit powers, thereby protecting against the unknown forces of the universe by prevailing upon their potential beneficence in all matters relative to life.
Masks: Reflections of Culture and Religion . So in religious ceremonies involving masks, the mask and the wearer either represents a good spirit or an evil spirit.
In the West, identity masks are only used at Halloween, Mardi Gras, or costume parties. The mask allows the wearer anonymity to release inhibitions. In other words, the mask wearer feels free to behave as they really want to, to do things under the cloak of anonymity. I'm pretty sure this doesn't bring out the virtue in people. Their real self is unmasked while wearing a mask. “A mask is not to disguise who you are but to show who you really are.” - Chloe Thurlow .
Of course, masks do not have to be physical. Many cultures have the mask of alcohol or other drugs, which lower inhibitions, that is unmasking the real self. Many people use a mask of anger to hide fear, weakness, shame, or embarassment - Psychology In Everyday Life . Humor can also be used a a mask - Masking Depression With Humor . In religion, tradition can be a mask - Behind the Mask of Religious Traditions . Masks can work two ways, hiding the real self or revealing the real self, or perhaps who the wearer wants to be.
Masks and the Theater
Heavily coiffured and of a size to enlarge the actor’s presence, the Greek mask seems to have been designed to throw the voice by means of a built-in megaphone device and, by exaggeration of the features, to make clear at a distance the precise nature of the character. Moreover, their use made it possible for the Greek actors—who were limited by convention to three speakers for each tragedy—to impersonate a number of different characters during the play simply by changing masks and costumes. Encyclopedia Britannica 
What were those Greek actors called? Hypokrites, from which we get the English word hypocrite.
It took a surprisingly long time for hypocrite to gain its more general meaning that we use today: “a person who acts in contradiction to his or her stated beliefs or feelings.” - Merriam Webster 
Masks and the Bible
Putting on a mask to portray or become an evil spirit is simply bad.
Putting on a mask to appear righteous is also bad.
Portraying an evil spirit allows the evil side of a person to come out and be revealed.
4 Ways to Identify a Wolf in Sheep’s Clothing .
Are masks mentioned in the Old Testament? Possibly. In the story of the Golden Calf (Exodus 32), the people don't know what happened to Moses, they panic, and want a replacement for Moses, a replacement that isn't human and can serve as an intermediary between the people and God Himself. They had their chance to see and hear God directly at Mount Sinai, but they chose to have an intermediary instead.
Exod 32:1 Now when the people saw that Moses delayed to come down from the mountain, the people assembled about Aaron and said to him, "Come, make us a god [elohim] who will go before us; as for this Moses, the man who brought us up from the land of Egypt, we do not know what has become of him.
Rabbi David Fohrman  argues that "egel maseka" in Hebrew could be translated as molten calf or calf mask. The people wanted an intermediary that could survive a face to face encounter with God, like Moses did. The calf mask was a shield to protect them. Only it doesn't work that way, the mask is a perversion of the relationship with God, which must actually be face to face. The irony is that Moses ends up being the one who has to wear a veil (masveh) when talking to the people. Moses face shone after forty days on the mountain with God, and when he came down, the people were afraid of him, so he wore a veil, not because he wanted to hide his identity. It's not clear to me how long Moses wore the veil, perhaps for the entire 40 years Israel wandered in the desert.
[paragraph added Mar 21, 2018]
I missed an important connection between masks and the commandment that says - "You shall not take the name of the LORD your God in vain, for the LORD will not leave him unpunished who takes His name in vain" - Exodus 20:7. A reader commented that this verse is really talking about hypocrisy, that is taking God's name in vain is more than using swear words. He paraphrased it like this "You shall not just act like you are one of God's people; for the LORD will not hold him guiltless that bears his name in vain." Taking or bearing God's name has to be sincere, not a mask worn for the praise of men.
Masks and the Christian
God hath given you one face and you make yourselves another. - William Shakespeare, Hamlet