CPI is released at 8:30 a.m. Eastern, usually mid-month. Headline CPI includes everything; core CPI excludes food and energy and is what the Fed watches more closely. Both are quoted month-over-month and year-over-year.
Because inflation drives fomc decisions, CPI has become one of the largest market-moving releases. A tenth of a percent above or below consensus can move es 1% or more.
Example: consensus core CPI is +0.3% month-over-month. The print is +0.4%. Rate-cut odds fall, yields rise, and the Nasdaq drops 1.5% in the first ten minutes.
Related: fomc, nfp, economic-calendar, federal-funds-rate