Diffie-Hellman key exchange
Suppose you want to exchange secret information with an associate. You agreed on an encryption algorithm, but you still have to exchange keys. This is tricky, because anyone who can intercept the keys as they are exchanged can decipher all of your messages.
It turns out you can agree on a secret key without anyone being able to intercept it. Magic? Not quite, though without knowing the mathematics behind it it may look like it is. Check out the Diffie-Hellman key exchange.