Like so many English words, it derives from Latin. To best understand what it means, go back to the Latin roots. (There are websites for this. The key word is "etymology".) All of the modern meanings come directly from the roots:
"Ex" = from, forth
"ponere" = put, place
So it means to "put forth", or in current lingo to "reveal", "explain", and so forth. For a long list of such words, use a thesaurus (also available online) to find a long list of synonyms for "expose". All of them mean something close to "put forth".
I agree with what Sunny said.