Convenience yield is a basic concept in the pricing of futures, with underline asset a commodity which can be held for consumption. It is estimated as a percentage annualized return (like interest rates) that the commodity can earn if held in a storehouse in order to be instantly deliverable if needed. This return can arise from speculation on temporary shortages or use in the production process.
In other words, it reflects the expectations of market participants relatively to the future availability of the commodity. Apparently, futures with underline assets that can’t be used for consumption don’t incorporate convenience yield.
The relationship between futures prices and the convenience yield is inverse. This means that when the convenience yield is rising the future price is falling and vice versa. This is logical, because in order to response to supply shortage someone must have the asset handy and not wait for it to be delivered in a distant date and in that way the demand for futures is falling hence their price. This is also obvious in the valuation formula of commodity futures held for consumption (negative sign in front of y).