In normal times, the ECB decides on the appropriate level of the short-term interest rate and provides the necessary liquidity to make such a rate prevail in the overnight market. A forecast of the necessary amount of liquidity is based on the need for liquidity by banks at the aggregate level.
And the money market fulfils the task of distributing the liquidity across individual banks in an efficient manner as the banks themselves provide intermediation. In normal times, the change in the overnight rate is then transmitted to the whole array of interest rates via arbitrage and somewhat predictable relationships, both along the intertemporal dimension and the intra-temporal dimension.