How does money on chain works?

As a practitioner in the realm of cryptocurrency and finance, I'm curious to understand the fundamentals of how money on a blockchain actually works. Could you elaborate on the mechanisms that enable digital currencies to function securely and efficiently on a decentralized ledger? Specifically, I'm interested in understanding how transactions are validated, recorded, and secured on the blockchain, as well as the role of consensus algorithms and mining in maintaining the integrity of the ledger. Additionally, I'd like to know how cryptocurrencies enable value exchange without relying on traditional financial institutions or central authorities.