To understand the revolutionary impact of cryptocurrencies you need to consider both properties. Bitcoin as a permissionless, irreversible, and pseudonymous means of payment is an attack on the control of banks and governments over the monetary transactions of their citizens. You can‘t hinder someone to use Bitcoin, you can‘t prohibit someone to accept a payment, you can‘t undo a transaction.
In 2014, researchers at the University of Kentucky found "robust evidence that computer programming enthusiasts and illegal activity drive interest in bitcoin, and find limited or no support for political and investment motives". Australian researchers have estimated that 25% of all bitcoin users and 44% of all bitcoin transactions are associated with illegal activity as of April 2017. There were an estimated 24 million bitcoin users primarily using bitcoin for illegal activity. They held $8 billion worth of bitcoin, and made 36 million transactions valued at $72 billion.
Every transaction is a file that consists of the sender’s and recipient’s public keys (wallet addresses) and the amount of coins transferred. The transaction also needs to be signed off by the sender with their private key. All of this is just basic cryptography. Eventually, the transaction is broadcasted in the network, but it needs to be confirmed first.