ACID: Atomicity, Consistency, Isolation, and Durability
They are considered to be the key transaction processing features/properties of a transaction System (eg. a database). Without them, the integrity of the System cannot be guaranteed.
Atomicity
Refers to the ability of the System to guarantee that either all of the tasks of a transaction are performed or none of them are. For example, the transfer of funds can be completed or it can fail for a multitude of reasons, but atomicity guarantees that one account won't be debited if the other is not credited as well.
Consistency
Refers to the System being in a legal state when the transaction begins and when it ends. This means that a transaction can't break the rules, or integrity constraints, of the system. If an integrity constraint states that all accounts must have a positive balance, then any transaction violating this rule will be aborted.
Isolation
Refers to the ability of the application to make operations in a transaction appear isolated from all other operations. This means that no operation outside the transaction can ever see the data in an intermediate state; a bank manager can see the transferred funds on one account or the other, but never on both?even if she ran her query while the transfer was still being processed. More formally, isolation means the transaction history (or schedule) is serializable.
Durability
Refers to the guarantee that once the user has been notified of success, the transaction will persist, and not be undone. This means it will survive system failure, and that the System has checked any integrity constraints and won't need to abort the transaction. Typically for databases, all transactions are written into a log that can be played back to recreate the system to its state right before the failure. A transaction can only be deemed committed after it is safely in the log.