The issue that Krugman is trying to explain is that inflation is not an objective, verifiable fact about the world, universal from all points of view.  Rather, inflation is something that individuals experience differently based on the kinds of things they want to consume or have to consume. How one measures inflation is thus dependent upon the question one is really asking and upon the political arguments one is trying to make. Do you want to know whether poor renters are facing higher prices relative to wages, or do you want to know whether more productive economic agents are facing higher prices? (Are you interested in welfare and equity, or are you interested in economic growth?)

What Krugman is explaining here that central bankers, whose job is to try to match the money supply to the amount of real things produced and consumed in the world, are going to be more interested in core inflation, without food and energy noise in the mix.  The reason is because food and energy are classic supply and demand commodities whose price movements reflect changes in real supply and demand conditions more than other things, so higher food and energy prices usually don't mean that too much money is being printed.  Higher oil prices, Krugman is arguing, is not due to monetary issues but rather due to perceived shortages of oil. Central bankers shouldn't worry about oil prices when determining whether to print more, or less, money, just the prices of things that don't fluctuate so much with supply and demand changes, such as wages.