I'm gonna sound like a major newbie here....but does proof mean not ever touched by anyone? If so, how do they move the coins or even put them in a regular coin folder?
"Proof" refers to the method by which the coins are created. The U.S. and many world mints specially prepare highly polished dies, and usually strike coins with greater pressure than the standard business or circulation strikes, on specially prepared cleaned and polished planchets. Many times they are struck twice to ensure lots of detail. Because of their highly polished surfaces, proofs are easily susceptible to being marked, and should always be handled only by the edge, and only while wearing soft white cotton gloves. BTW - There isn't anyone on this forum who wasn't a "major newbie" once upon a time.
Proof is a method of manufacture. Proof coins are struck with specially made dies and special planchets which are highly polished as a general rule. Then the planchets are struck with higher pressure than normal coins - and then struck again. This produces the high degree of detail and quality of strike. As for the coins being touched - in todays mints machines do the job. They take the coin right out of the striking chamber and place them into packaging for sale.