Public-key cryptography

Public-key cryptography splits a key into two halves that belong together. One you publish to the world, one you never show anybody.

The clever part is that what one half does, only the other half can undo. So anyone can lock a message using your public half, and only you can open it. Or you can sign something with your private half, and anybody can check it really came from you. It is what makes it possible to communicate securely with somebody you have never met and never agreed a password with, which is most of the internet.