1) Increase in prices because of increase in money supply

2) Increase in prices because of supply shocks (weather, strikes, supply chain, disruption) or unusual spiky demand.

Core CPI is an attempt to measure (1) to ensure the money supply, which the fed controls is at balance (with their other mandate of full employment).

It's a hard problem because there are lot of nuances and still we want to measure the same thing for a fair MoM or YoY comparison.