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A blockchain is fundamentally a data structure that acts as a ledger with three key properties: consensus, persistence, and liveness.
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Consensus means all participants agree on the data stored on the blockchain, with minor exceptions for the most recent entries.
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Persistence ensures that once data is added, it cannot be removed, assuming certain limitations on adversary computing power.
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Liveness guarantees that anyone can add data to the blockchain and the system will not get stuck.
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Blockchains enable currency systems by ensuring everyone agrees on transaction history and account balances, while preventing transactions from being arbitrarily undone.
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Persistence is achieved in a distributed system through widespread data replication across miners, end-users (via wallets), and service providers, making it extremely difficult to revert states.