Definition: Core inflation, or core CPI, is important because this is what the Federal Reserve looks at to decide whether or not to change the Fed Funds rate. Core inflation is simply the BLS's Consumer Price Index (CPI) minus food and energy prices.
The Fed uses the core CPI because food and energy, specifically gasoline, prices are so volatile month-to-month. On the other hand, the Feds tools are so slow-acting. It can take six - 18 months before the effect of a rate change can trickle down into the economy.
For example, inflation increases during the summer, when gas prices increase due to the vacation driving season. However, the Fed would not want to increase interest rates every summer. Instead, it must wait to see if those increases drive up the prices of other goods and services.

