The reason is simple if one considers a typical hard (non-perishable) commodity such as gold. It is preferable to enter into a forward contract than to invest in buying the commodity itself.
The holder of a future or forward will benefit from any gains in the price of the underlying. That gain can be realised either by selling the commodity after delivery of the future, or by selling the (now more valuable) future in the meantime. At the same time, the holder of a future has not put down money to buy the commodity, and can therefore can receive interest on the money thus saved (compared to buying the commodity).
The situation is slightly more complex for futures on financial assets. Futures on securities (uncommon, as options are usually preferred) are affected by dividend payments and similar benefits. In the case of currency forwards, both parties continue to receive interest so the relationship between the spot and forward prices is related to the interest rate differential (see interest rate parity). In neither case can forwardation be assumed.
Forwardation does not always hold for soft (perishable) commodities due to factors such a seasonal demand and supply cycles.