Article's a bit too "wordy" for me. And the spelling of consistency wasn't consistant! ;-)
Atomicity states that database modifications must follow an “all or nothing” rule. Each transaction is said to be “atomic.” If one part of the transaction fails, the entire transaction fails. It is critical that the database management system maintain the atomic nature of transactions in spite of any DBMS, operating system or hardware failure.
•Consistency states that only valid data will be written to the database. If, for some reason, a transaction is executed that violates the database’s consistency rules, the entire transaction will be rolled back and the database will be restored to a state consistent with those rules. On the other hand, if a transaction successfully executes, it will take the database from one state that is consistent with the rules to another state that is also consistent with the rules.
•Isolation requires that multiple transactions occurring at the same time not impact each other’s execution. For example, if Joe issues a transaction against a database at the same time that Mary issues a different transaction, both transactions should operate on the database in an isolated manner. The database should either perform Joe’s entire transaction before executing Mary’s or vice-versa. This prevents Joe’s transaction from reading intermediate data produced as a side effect of part of Mary’s transaction that will not eventually be committed to the database. Note that the isolation property does not ensure which transaction will execute first, merely that they will not interfere with each other.
•Durability ensures that any transaction committed to the database will not be lost. Durability is ensured through the use of database backups and transaction logs that facilitate the restoration of committed transactions in spite of any subsequent software or hardware failures.