What is diffie-hellman most commonly used for?

DH is an algorithm to derive a shared secret over an unsafe channel.

Both parties exchange public keys, and can join them together with their private keys to create the secret. An eavesdropper can see both public keys, but since he doesn't posess the private keys, cannot derive the same secret.

The secret can be used to subsequently encrypt communications with a symmetric algorithm.

TLS uses this approach.