Typically, in options or futures trading, positions that expire further in the future carry a premium over positions that are relatively short-term. This structure represents the usual order of things, because bets that can't pay off for a while carry more risk.
The further in the future a contract expires, the more stuff that can happen to mess things up. Plagues, locusts, frogs falling from the sky...whatever. As such, investors usually demand compensation for their trouble if they're asked to wait for a longer period of time before they can recognize a profit.
As you've probably guessed by now, an inverted market represents the opposite set of these usual circumstances. An inverted market, or a market in backwardation, as it's sometimes called, is characterized by contracts with a near-term expiration carrying a higher premium than contracts with expirations further out in the future.
In an inverted market, investors are getting a higher price for stuff happening soon, rather than stuff happening later...the opposite of normal.
An inverted market can happen when near-term supplies of a commodity are disrupted. The long-term outlook for the product looks generally the same...but the spot market skyrockets because of a short-term shortage.
Example time.
You speculate in pork belly futures. One day, the Pig Slaughters Union of America goes on strike and all the slaughterhouses close down. Suddenly, there's a shortage of pork bellies. Near-term prices skyrocket. However, longer-term prices stay more stable, because investors assume that the labor dispute will be resolved relatively soon. An inverted market for pork bellies results.