Overview
Double spending is a problem unique to digital currencies. Unlike physical cash, digital data can be easily copied. Without a central authority (like a bank) to verify that a user has the funds, a malicious actor could try to send the same digital token to two different recipients simultaneously.
Blockchain Solution
Blockchain solves this by requiring all transactions to be recorded on a public, immutable ledger. Before a transaction is confirmed, the network's nodes check the history of the ledger to ensure the sender hasn't already spent those specific funds. Once a transaction is included in a block and followed by several more blocks, it is considered 'final' and impossible to double-spend.
Attack Vectors
Double spending is usually only possible during a 51% Attack or a Race Attack (where an attacker sends two conflicting transactions very quickly).