Now there's some terms you don't see everyday.
These two terms describe conditions in the futures markets. Contango is the normal condition in which things will cost more in the future than now. It is normal because it includes the costs of storage of the real commodity, and the money value of lost interest realized by paying now instead of later. And increasingly in our society the probable effect of inflation of the currency.
Backwardation on the other hand is a bellwether of things to come. If a precious metal like say silver was trading at $16/oz for immediate delivery and trading at $14/oz six months out, the prudent thing to do would appear to be sell your silver now and re-buy it now for delivery in a half year, pocket the $2000 or $20,000 stick it in a CD drawing interest,and retrieve your silver in six months avoiding the storage fees. But it doesn't happen. Or rather it doesn't happen until the difference is sufficient. Why? Because of the risk that you will not be able to retrieve your purchase, and the risk that the money you have drawn off your transaction will have inflated (read devalued) to a greater extent than your gain.