"Tâtonnement" is an economics term which describes an iterative auction process that aims to maintain a state of equilibrium with respect to trades.
The word is borrowed from French where it can mean "groping" or "trial and error".
Ethereum's London Upgrade introduced variable block sizes.
Each block has a target size of 15 million gas which the protocol tries to maintain via tâtonnement. It does this by changing the base gas fee for the next block.
If the current block size == 15M gas, the next block's base fee will stay the same.
If the current block size > 15M gas, the next block's base fee will be increased.
If the current block size < 15M gas, the next block's base fee will be decreased.