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If it is foreign exchange futures, then the basis is the difference between the current futures price and the current spot rate. The basis risk is the fact that the basis will change over the life of the future.
If it is interest rate futures, then the basis is the difference between the current futures price and the current interest rate expressed as a future. Again, the basis risk is the fact that the basis will change over the life of the future.
(We always assume that the basis will fall linearly to zero over the life of the future in both cases.)
All of this is explained in detail in my free lectures on foreign exchange risk and interest rate risk – I cannot type out all of the lectures here 🙂
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