The Consumer Price Index measures how much the average price of a fixed basket of goods and services — food, rent, fuel, healthcare — changes over time. When economists or traders say "inflation," CPI is usually the number they mean.
For currency markets, CPI matters because central banks set interest rates partly in response to it. A higher-than-expected print tends to push central banks toward a more hawkish stance (supportive of the currency); a lower-than-expected print eases that pressure (more dovish).
Headline CPI includes everything — food and energy included. Core CPI strips both out, because they swing for reasons that often have little to do with the underlying economy (a war affecting oil prices, a poor harvest). Central banks weight core CPI more heavily for exactly that reason — it's a steadier read on where prices are actually trending.
CPI is released on a fixed schedule against a consensus estimate from economists. It's usually the gap between the actual print and that consensus — not the absolute level — that moves currencies in the minutes after release, because the consensus is already priced in beforehand.