This is the key selling point of Monero. While it relies on a public ledger (blockchain), it makes all transactions private by using a set of tools, including Ring Signatures, Stealth Addresses and RingCT. These technologies are quite complicated, and in the following few paragraphs we’ll try to explain them in plain English:
Ring signatures – this piece of technology bundles every transaction into a group with other seemingly identical transactions, making it virtually impossible for an outsider to tell which source of money is the real one. In other words, Ring signatures hide where the money is coming from.
Stealth Addresses, on the other hand, hide who the money is being sent to by generating a one-time random address unique to the recipient. Whilst anyone can view these addresses, there is no way to make a link between this address (public key) and the recipient’s real address (private key).
Last but not the least, RingCT (Ring Confidential Transactions), hides the amount being transferred. Implemented in January 2017, it was first optional and is about to become mandatory for every transaction.