Paul Krugman has a review posting explaining the concept:
Core inflation isn’t supposed to measure the cost of living, it’s supposed to measure something else: inflation inertia.
Think about it this way. Some prices in the economy fluctuate all the time in the face of supply and demand; food and fuel are the obvious examples. Many prices, however, don’t fluctuate this way — they’re set by oligopolistic firms, or negotiated in long-term contracts, so they’re only revised at intervals ranging from months to years. Many wages are set the same way.
Why the review? Because we're becoming like more Japan in the 1990s:
[I]nflation tends to be self-perpetuating, unless there’s a big excess of either supply or demand. In particular, once expectations of, say, persistent 10 percent inflation have become “embedded” in the economy, it will take a major period of slack — years of high unemployment — to get that rate down. Case in point: the extremely expensive disinflation of the early 1980s.
...And what these measures show is an ongoing process of disinflation that could, in not too long, turn into outright deflation.
It's not quite end-of-the-world stuff, but it does make one nervous.