As food and energy prices (22% of the CPI) can be very volatile month-to-month, focus on the core CPI. Rising core CPI, may indicate an overheating economy, which would prompt the Fed to raise interest rates. One would also want to look at the components of the CPI, to determine if price pressure is general, or narrow. General price increases are more likely to prompt Fed action than narrow ones, which may represent temporary cost distortions.
In the modern era, there is less of a direct link between CPI and central bank policy. Interestingly, central banks try to change their policy stance in a pre-emptive fashion. That is, they prefer to respond to inflation ‘pressures,’ rather than to inflation itself.