to show: to cause someone to see or perceive something, whether by putting it before their eyes, revealing it, explaining it, or proving it
At its core this verb means to make something perceptible to another person. The plainest use is physical: you hold a thing up, point it out, or present yourself so that someone can see it, as when a healed man is told to go show himself to the priest.
From that literal act the word stretches naturally in three directions, and the senses below are shades of the same idea rather than separate words. It can mean to reveal something otherwise hidden, which is its dominant use in the visions of Revelation, where an angel shows John what is to come. It can mean to make a truth known by explaining it, as when Jesus begins to show his disciples that he must suffer. And it can mean to prove or demonstrate a claim by producing the evidence, as in the challenge to show your faith by what you do.
What holds these together is that in every case something is being brought into another person's view. Whether the object is a coin, a heavenly city, a coming event, or the reality of a person's faith, the word asks the hearer to look and see. English handles the whole range with the single word show, though that convenience can flatten the difference between simply displaying a thing and revealing a mystery.