What is "Diffie-Hellman key exchange" and how does it work?

Have you heard of The Two General's Problem? The Diffie-Hellman key exchange is a solution to this problem to allow for the secure exchange of cryptographic keys over an encrypted channel.

It works using public/private key pairs (asymmetric encryption). Two parties that wish to communicate securely over a public channel will each generate a public/private key pair and distribute the public key to the other party (note that public keys are free to be exchanged over a public channel). From here, each party can derive a shared key using a combination of their personal private key and the public key of the other party. This combined key can now be used as a symmetric encryption key for communications.