Advanced cryptography. OTOH:

* Each transaction is signed by a "ring signature", where it's known that 1 of a set of 8 keys signed the transaction, but not which one. This is your actual input plus 7 other random inputs drawn from the same probability distribution as actual inputs.

* Double-spending is prevented by a "key image" which is something mathematically related to your actual key (not sure how that's verified without knowing which key it is). Each key image can only be used once, or it's a double-spend.

* Input amounts and output amounts have to balance using some kind of zero-knowledge proof.

It doesn't.

When you make a transaction on the Monero network, only the actual sender and recipient know the sender, recipient, or value of the transaction. This makes tumblers unnecessary and removes that whole ethical burden. If your Monero is ethically sourced (i.e. you mined it or bought it with your own money) then you can safely spend it without being subject to any tracking.