I’m embarrassed by how little I remember from my “Intro to Crypto” class at Stanford. This video really helped: https://www.youtube.com/watch?v=wXB-V_Keiu8.
It talks a little about the history of encryption — until the 1970’s symmetric key encryption was used. Public key encryption was quite the breakthrough. And get this — when it was first discovered (invented?) the THE GOVERNMENT INSTANTLY CLASSIFIED THE RESEARCH!!! It was later re-discovered.
Anyway, for laypeople, I’d suggest watching this video to the point of understanding that it’s really, really hard to factor the product of two big prime numbers.
Trying to understand the Modular function which stands on top of this fact is difficult.
Final note: Though it isn’t in the video, my understanding is that Bitcoins don’t actually encrypt anything, but they use these crypto algorithms to verify that transactions match account numbers. Digital signatures, in other words.
So, if you post your bitcoin account number on a website to accept donations, everyone who uses bitcoins can see what transfers were made to that account. Of course, the beauty of bitcoins is that you can make as many accounts as you want and transfer bitcoins between them.