It's part of the oh-so-arcane Bitcoin lingo that's way too contemporary for its own good.
Double spending refers to an “attack” where a given set of coins is spent in more than one transaction. There’s always one in every crowd who tries to game the system with a double spend. The primary manner in which to accomplish this feat is to send two conflicting transactions in rapid succession into the Bitcoin network.
For example, let’s say you have 10,000 Bitcoins to spend. You buy a new phone from your Bitcoin wallet and immediately turn around and buy a tablet computer using those same 10,000 Bitcoins. You do it so quickly the system does not have time to catch your mischief. Most of us probably feel like we double spend on a daily basis with only one paycheck, but so many wonderful ways to spend it beyond that amount. But double-spending is unique to digital currencies, and hopefully there are Bitcoin police around to boot the transgressors out of the network.