Tornado.cash is an addition to the Ethereum arsenal of tools allowing transaction privacy and anonymity in a non-custodial fashion, making use of zkSNARKs and breaking the on-chain link between recipient and destination addresses. It makes use of a contract which accepts an Ether deposit which can then be withdrawn by different addresses with no way to link the withdrawal to the deposit. To ensure untraceability it is advisable to use a VPN or some other available means for concealing one's actual geotraceable IP address (which the Tornado interface detects and shows in the lower right corner, as shown below).
To make a deposit a secret is generated and its hash (referred to as a commitment) sent together with the deposit amount to the Tornado on-chain contract, which accepts it and adds it to its list of deposits. Then, to make a withdraw the user has to provide a zero-knowledge cryptographic proof of possession of the secret to the unspent commitment to the contract. zkSNARK technology makes it possible to do that without revealing which deposit corresponds to the particular secret — the contract will check the proof and if valid, transfer the deposit to the withdrawing address, without anybody being able to determine which deposit it comes from.
There are two withdrawal options — using a wallet like MetaMask or transferring via a relayer. The first option requires that you have a new address with some Ether in it (to pay for network fees), which poses the question of how to avoid that Ether being traced to you and the transaction from the Tornado contract. Which is why the relayer option is available.
This is in effect similar to a mixer service but using other means for the purpose. Exchanging back and forth with Monero has been another widely used tactic (using services like Shapeshift for some time until it became noticed and Shapeshift introduced registrations and KYC/AML policies), but Tornado seems well suited for most purposes and, as most things Ethereum, comes with an elegant and easy to use interface.
