A defining aspect of cryptocurrencies is that is it now possible to complete a monetary transaction without need to assume trust in a third party. In traditional finance, a monetary transaction on the internet requires trust in a facilitator such as central banks, commecial banks, agents, or financial service provider without the universal access to audit their ability to faciliate the transaction. Sending money online is more akin to writing a cheque than paying in cash as the issue of decentralization without double spending remains unsolved until the emergence of bitcoin.
When a party makes a transaction with cryptocurrencies, they can verify publically and mathematically that a transaction has been completed. This is in contrast to taking the "transaction completed" notification from a facilitator at face value.