Sometimes when you are in doubt, go to reddit, and this is one example of why. I came across this gem of an explanation of cryptography in its essence, and full credit goes to UlyssesSKrunk.
Take your message, treat it as a number and multiply it by a bunch of primes. Send it to me. I will then multiply by a bunch of primes too. I send it back to you. You then divide by all of your primes. Send it back to me. I divide by all of my primes and get the original message. It may be easier to think of the message as a box and the primes as locks. You want to send a box to me without Eve getting at what’s inside. So you put a lock on it and send it to me. Now neither Eve nor I can open it because it’s locked. I add my own lock because fuck you and your stupid lock. I send it back to you. Now you can’t open it and it’s locked so it’s worthless, therefore you take your precious lock back and send the now worthless piece of shit back to me. Eve is still like “WTF?” All she has seen so far is the same box going back and forth with locks she can’t open. So now I get the box with my lock on it and I take my lock off. Now the box is unlocked and I can take your shit.