This is a zero-disclosure proof protocol (English Zero-Knowledge Proof), in cryptocurrencies it is used as a way to confirm transactions between users without disclosing details of the transfer being performed.
Due to the Zero-Knowledge Proof, you can perform transactions in which a third-party observer will not be able to see the addresses of the sender, the recipient and the amount of the transfer. The basis for achieving consensus is the principle when the verifier can be convinced of the veracity of the statement on indirect grounds.
For example, an unknown person wrote to Bob and introduced himself to Alice. Bob, in order to check with whom he actually communicates, sends an encrypted message that can be decoded only with Alice's private key and asks what was in the message. If Alice is real, then she will easily give Bob the correct answer and thereby confirm her identity, while not revealing the address from which she contacted. Theoretically, not a real Alice can just guess the right answer and fool Bob. But Bob can repeat the test many times, thereby reducing the possibility of cheating to almost zero.
The first cryptocurrency that applied this algorithm was Zcash, it is also used in its forks. A variant of a zero-disclosure proof called Bulletproofs recently activated the Monero project. Also, work is underway on the implementation of the Zero-Knowledge Proof in the Ethereum blockchain.