Diffie and Hellman wanted to make Transport Layer Security (TLS), a secure way of computers communicating, more safe to perform. For example, while you can use a password to keep a file safe, if you need to tell the password to somebody there is a risk of the password being seen by third parties. Diffie-Hellman key agreement itself is an "anonymous" (non-"authenticated") key-agreement protocol: people involved in the trade do not need to prove who they are, but both people need to use their secret keys to fully decrypt the data. 