Cryptos use blockchain or similar electronic ledgers. In private cryptocurrencies, there is no control issuing authority. The blockchain is used for crowd-sourced verifications of the authenticity of transactions.
Every crypto coin mined has a unique code. In case of Bitcoin, it can be broken down into a hundred million different unique codes, and that code is associated with the specific wallet that contains the coin.
When a crypto transaction is made, the crowd reviews the blockchain to ascertain whether a wallet that possesses a specific coin is transferring that coin to a different wallet. Literally, each and every transaction made can be reviewed. Thus history of every specific coin can be traced.
Here there is anonymity of transaction because the owner of a digital crypto wallet need not be known. Any entity could own any number of crypto coins.