For example, a server might have some encrypted logs or storage or whatnot, that would only be used for reference later. This way even if the server is hacked, everything is still OK until the hacker comes up with a way to intercept the data before encryption.
Another example is the basic browser HTTPS/TLS model where it needs to securely talk to an unknown server and they have no prior key exchange,, without an eavesdropper getting the necessary keys. I almost had an answer in this question: How secure is SSL?, but I still have more reading to do before I understand, but what caught my attention the most was the last answer (no upvotes or comments, just a high rep user)
Whether it relates to SSL or not, and whether that last answer is correct or not, I also want to know if it is possible to create an encryption-only key that requires brute force to decrypt. I don't see how this is possible yet.