Modern cryptography is fundamentally concerned with the problem of secure private communication.
If Alice and Bob are able to meet, privately, beforehand, and agree on some common secret key, then it becomes easy for them to achieve such private communication. But Alice and Bob might not be able to first meet in private and agree on a key. In this case, we ask under what assumptions they can still agree on a common secret key, where their conversation is conducted entirely in public. A Secret Key Exchange is a protocol where Alice and Bob, having no secret information in common to start, are able to agree on a common secret key, conversing over a public channel. Secret Key Exchange is of course trivial if trapdoor permutations exist.