The best way to explain this is for me to take a ATM withdrawal as an example. Once you draw money from a ATM, the transaction is recorded on the Banks internal ledger and they can identify the person linked to that withdrawal. If they recorded the serial numbers on the cash, they can track who withdraw that money and if they follow you, then they can track where that money goes.
So what you do is, you spend that money at a merchant and you get change and that change can then not be tracked, because someone had to record the serial numbers of all the money that was used at that merchant.
The same happens with Mixers or Tumblers, because they mix your coins with other people's coins and put them back onto the Blockchain <Bitcoin's onchain ledger system>
<Most of them, say that they destroy all records of the mixing of the coins>
