As clearly seen here, Bob is tendering a $10 bill to Lisa in exchange for a book. Once Lisa receives this physical $10 bill, there is no way for Bob to re-use this money for some other transaction, as the physical currency is now in Lisa’s possession.
Now, consider a situation where the money is paid in Digital form.
Because the money transaction format is in digital form, it is essentially a single physical file saved somewhere on Bob's device. Bob can send a copy of this file (digital money) to Alice after he gives it to Lisa. Both now believe they have received the money despite the fact that they have no way of certifying the digital coin, and they intend to deliver their items to Bob. This is known as double-spending, and it occurs when a sender spends the same amount of money in various places to receive services or items from multiple vendors.
To solve this problem of double-spending, one would employ a centralized authority to monitor all the transactions.
The central authority, which is commonly referred to as your bank, keeps a record of all transactions in a ledger book. Bob now needs to submit his digital money to the bank, which will debit Bob's account in its ledger. After verifying that Bob has sufficient funds to cover the cost of the digital money wishes to send, the money would be sent to Lisa and credited to her account in the ledger.
It is now certain that Bob will not spend the money twice. The problem of double-spending would be overcome if every digital transaction was routed through a centralized authority like this. Another advantage is that itcan verify the legitimacy of each coin (digital money) it gets throughout the transaction. As a result, the counterfeit money (duplicate) Money would be easily identified and removed from circulation (as in the scenario of Bobpaying Alice with a copy).
The introduction of centralized authority though it solves the double-spending problem, introduces another major issue - the cost of creating and maintaining the centralized authority itself.
As the banks need money for their operations, they start cutting commissions on each currency transaction they do for their clients. This sometimes can become very expensive, especially in the overseas transfers of money where multiple agents (banks) may be involved in the entire deal.
All the above issues are solved by the introduction of digital currency, called Cryptocurrency.
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