When you choose to upload your images to iCloud (which currently happens without end-to-end encryption), your phone generates some form of encrypted ticket. In the future, the images will be encrypted, with a backdoor key encoded in the tickets.
If Apple receives enough images that were considered a match, the tickets become decryptable (I think I saw Shamir's Secret Sharing mentioned for this step). Right now, Apple doesn't need that because they have unencrypted images, in a future scheme, decrypting these tickets will allow them to decrypt your images.
(I've simplified a bit, I believe there's a second layer that they claim will only give them access to the offending images. I have not studied their approach deeply.)
