Double-spending is the risk that a digital currency can be spent twice. It is a potential problem unique to digital currencies because digital information can be reproduced relatively easily by savvy individuals who understand the blockchain network and the computing power necessary to manipulate it.
Physical currencies do not have this issue because they cannot be easily replicated, and the parties involved in a transaction can immediately verify the authenticity and past ownership of the physical currency.
Bitcoin has a mechanism based on transaction logs, known as the blockchain, to verify the authenticity of each transaction and prevent double-counting. Bitcoin requires that all transactions, without exception, be included in the blockchain. This mechanism ensures that the party spending the bitcoins really owns them and also prevents double-counting and other fraud.