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Atomicity – a transaction to transfer funds from one account to another involves making a withdrawal operation from the first account and a deposit operation on the second. If the deposit operation failed, you don’t want the withdrawal operation to happen either.
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Consistency – a database tracking a checking account may only allow unique check numbers to exist for each transaction
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Isolation – a teller looking up a balance must be isolated from a concurrent transaction involving a withdrawal from the same account. Only when the withdrawal transaction commits successfully and the teller looks at the balance again will the new balance be reported.
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Durability – A system crash or any other failure must not be allowed to lose the results of a transaction or the contents of the database. Durability is often achieved through separate transaction logs that can “re-create” all transactions from some picked point in time (like a backup).
(summary of the real world examples from le dorfier’s link)