Race Attack, as the words strongly suggest, pertain to two transactions being created with the same funds and at the same time. The intention behind this creation is the allowance of spending those funds twice.
This action is perpetuated by an attacker of a blockchain. The first of the transactions he or she had created would be sent to the victim who would be accepting the payment and sends the product without the benefit of a transaction confirmation.
The second transaction, the conflicting one, would reflect the same amount sent to the attacker. It would then be disseminated to the network. This will make the first transaction invalid and therefore immaterial.