The Basics
RingCT, short for Ring Confidential Transactions, is how transaction amounts are hidden in Monero.
Ring CT was implemented in block #1220516 in January 2017. After September 2017, this feature became mandatory for all transactions on the network.
RingCT introduces an improved version of ring signatures called "A Multi-layered Linkable Spontaneous Anonymous Group signature", which allows for hidden amounts, origins and destinations of transactions with reasonable efficiency and verifiable, trustless coin generation.
For more information, please read the creator Shen Noether's paper here.