Core inflation = full (a.k.a. headline) inflation minus inflation in energy and food prices. It’s the number that monetary policy makers (like the Fed) look at when they are monitoring inflation.
Why would they ignore inflation in the two things that we all spend so much money on? The answer is that food and energy prices change all the time, in unpredictable ways. A war in the Middle East can cause oil prices to spike. A drought in the Midwest can devastate crops – reducing supply and increasing prices. But the Fed believes these are temporary events and temporary price changes. So they just ignore food and energy, and focus on the more lasting price changes of other things.