Let’s start with an oversimplified definition.
Basis = Future – Spot
Cobasis = Spot – Future
What we are trying to see is a measure of scarcity. If the price in the spot market is higher than in the futures market (e.g. grain, one week before the harvest) then the good is scarce. If the price in the futures market is higher, then anyone can “carry” the good at a profit. To “carry” means to simultaneously buy the physical good and sell a futures contract against it. A positive basis means this is profitable.
A positive cobasis means that it is profitable to “decarry”: to simultaneously sell the good in the physical market and buy a futures contract. Both carry and decarry result in the same position at the end of the day plus the profit from the spread.
To be precise, we must define these terms in a more complex way. Of course, to buy something one must pay the “ask” or “offer”. To sell, one must accept the bid. With that in mind, here are the correct definitions:
Basis = Future(bid) – Spot(ask)
Cobasis = Spot(bid) – Future(ask)
Note that both can be negative (which often occurs as a contract is heading into expiry and there is no liquidity, hence the bid is very low and the ask is very high). At most one of them can be positive. It can be profitable to carry a good, or to decarry it. But it makes no sense for it to be possible to carry profitably and decarry profitably!
There is a lot more to the theory of why these spreads are important and what they mean. You are likely reading this page right now because you hit a link from an article which discusses some aspect of it.