From time to time this manual mentions that transactions protect your data against 'system or application failure.' This is true up to a certain extent. However, not all failures are created equal and no data protection mechanism can protect you against every conceivable way a computing system can find to die.
Generally, when this book talks about protection against failures, it means that transactions offer protection against the likeliest culprits for system and application crashes. So long as your data modifications have been committed to disk, those modifications should persist even if your application or OS subsequently fails. And, even if the application or OS fails in the middle of a transaction commit (or abort), the data on disk should be either in a consistent state, or there should be enough data available to bring your databases into a consistent state (via a recovery procedure, for example). You may, however, lose whatever data you were committing at the time of the failure, but your databases will be otherwise unaffected.
Be aware that many disks have a disk write cache and on some systems it is enabled by default. This means that a transaction can have committed, and to your application the data may appear to reside on disk, but the data may in fact reside only in the write cache at that time. This means that if the disk write cache is enabled and there is no battery backup for it, data can be lost after an OS crash even when maximum durability mode is in use. For maximum durability, disable the disk write cache or use a disk write cache with a battery backup.
Of course, if your disk fails, then the transactional benefits described in this book are only as good as the backups you have taken. By spreading your data and log files across separate disks, you can minimize the risk of data loss due to a disk failure, but even in this case it is possible to conjure a scenario where even this protection is insufficient (a fire in the machine room, for example) and you must go to your backups for protection.
Finally, by following the programming examples shown in this book, you can write your code so as to protect your data in the event that your code crashes. However, no programming API can protect you against logic failures in your own code; transactions cannot protect you from simply writing the wrong thing to your databases.