meaning of the idiom " 64 dollar questions?

Answer 1

This is an shortened version of the proper "That's the $64,000 question!" It is the remnant of a scandolous TV Show of old. You can read a good history of it on the word reference site.

In short, the answer to your question is that it refers to an important question of which no one appears to know the answer. Likewise you will hear the term "That's the $64,000.00 answer!"