Double spending is a problem where the same amount of money is transacted with more than one time; thereby creating value out of thin air or causing other accountancy errors.
Blockchain solved this problem with the release of Bitcoin back in late 2008 / early 2009. Whenever a transaction is about to take place, a malicious actor can subvert a system by spending the same money on multiple things. Typically, two (or more) transactions will be executed at the same time. When this happens the system will register that X amount left this wallet and now locations A & B need to update their balances by X amount.