Alice downloads a snippet of music she likes from an untrusted source and wants to use it to find the name of the song.
Bob has a song recognition capability and could identify the song for Alice.
The problem is that Alice and Bob do not trust each other.
Alice fears that if she gives Bob her snippet of music, Bob might turn her into the authorities. Bob could give Alice his music catalog but fears that she may sell it to his competitors.
The solution is for Alice to encrypt her music snippet and send that to Bob. Bob could find the encrypted result and send that back to Alice to decrypt.