Yeah this is the right idea the fed sets interest rates to hit inflation target. This has to do with there ability to influence lending by setting there interest rates appropriately.
The whole idea being that if we have low interest rates we can lower the barrier to growth as much as possible without actually causing inflation but if the economy becomes constrained and the extra money is just chasing fewer things the fed has to increase interest rates to decrease free money so inflation doesn't spike. They honestly did a really good job too getting from 9%->3% is impressive and staying there despite the massive instability in pricy that Tariffs cause is a testament to that philosophy.
The whole idea being that if we have low interest rates we can lower the barrier to growth as much as possible without actually causing inflation but if the economy becomes constrained and the extra money is just chasing fewer things the fed has to increase interest rates to decrease free money so inflation doesn't spike. They honestly did a really good job too getting from 9%->3% is impressive and staying there despite the massive instability in pricy that Tariffs cause is a testament to that philosophy.