A double-spend is a set of actions that spends the same money twice. For instance, Mallory has 1 IOTA in her wallet. She could try to submit a transaction that will transfer 1 IOTA to Alice, and directly afterwards submit a transaction that transfers 1 IOTA to Bob. A cryptocurrence system must be able to detect this, and invalidate the last transaction (or both).

Reference: https://forum.iota.org/t/iota-double-spending-masterclass/1311/1