A double-spend transaction occurs when a digital transaction reuses previously spent "inputs" (funds) to make another payment.
The Bitcoin network's shared public ledger (the "block chain") solves the double-spend problem for digital transactions by removing double-spend attempts before they can be recorded as settled transactions. The possibility of double spending dramatically decreases with each Bitcoin network confirmation. Typically a payment with six confirmations can be trusted as fully safe from double-spend risk.
In rare, abnormal periods like Bitcoin protocol changes, there is an increased risk of deeper block chain reorganizations. These "reorgs" can make it harder to trust that even a payment with six confirmations is definitely not double-spent. This is why BitPay recommends that bitcoin users not send or receive funds during periods of bitcoin network disruption.