It works by lumping the coins of all the users together, breaking any direct connection between the endpoints of any given transaction.
Suppose Alice makes a deposit at the bank, but in the margin of the deposit slip she writes "for Bob". The cashier at this particular bank records a credit of $1000 from Alice, then prints and mails $1000 of cashier's checks to Bob, recording that series of debits as well. Later, the authorities raid the bank and seize its ledger. They can see a credit from Alice and a bunch of debits to Bob, but there is no transfer between Alice's account and Bob's account; this only proves that Alice could have paid Bob. If this bank has hundreds of other customers making similar transactions every day, it's basically impossible to use the ledger alone to prove any connection between Alice and Bob.
Now scale that up so that "the bank" is actually a consortium of banks that also perform a bunch of transactions among themselves to further obscure any associations among customers.
https://darknetmarkets.org/a-simple-guide-to-safely-and-effe...