Time Machine is Apple's built-in backup solution for OS X that creates hourly backups of all files on the system. Unlike a clone of the drive, the backups are not directly bootable, but they can be used to restore any instance of your OS installation and file structure to the drive. This makes it convenient for restoring data to a recently repaired system, migrating to a new one, or undoing a recent configuration change that is causing problems.
This backup solution is quite useful to have and is easy to set up, but there may be instances where Time Machine is configured to avoid important system files and thereby not create backups that can be restored to a bootable state.
Part of Time Machine's configuration is an exclusion list to which you can add files or folders to prevent them from being backed up. This is convenient for some large files, such as virtual machines, to prevent them from being continually backed up, but this feature also contains special handling for the Mac's system files. By default all files on the computer are backed up, but if you add the System folder to the exclusion list, then Time Machine will prompt you to have it not only avoid the system folder, but also other hidden folders on the system.
If enabled, this option will change a preferences setting in Time Machine to have it avoid these system files, which may seem preferable to some people, as it will reserve more Time Machine drive space for backups of your personal data, but it will result in the backups being unusable for restoring the entire system to a bootable state.
OS X will not remind you that it is only backing up your personal data and not the system, so unfortunately if Time Machine is set to omit system files, then you might not be aware of it until you run into a problem and need to restore your system. This may be especially true if, when checking out Time Machine's features, you enabled this option to try it out but then forgot it was set up.
Therefore, if you would like Time Machine to create backups that can be restored to a bootable state, then be sure that system files are not omitted. To do this, you can check your system in one of two ways. First, go to the Time Machine system preferences and see if you have either "\System" or "System Files and Applications" listed in the exclusion list. If so, remove these to ensure that they get backed up.
These being present in the list reflects Time Machine's hidden setting to avoid system files; however, in some instances this setting may be enabled even if these are not shown in the list. You can check for this by opening the Terminal and running the following command:
sudo defaults read /Library/Preferences/com.apple.TimeMachine SkipSystemFiles
If the output of this command is a 1, then Time Machine is set to avoid system files, in which case running the following command should clear the setting and allow Time Machine to create full system backups:
sudo defaults write /Library/Preferences/com.apple.TimeMachine SkipSystemFiles false
After this setting has been changed, keep in mind that when Time Machine next backs up it will now include your system files and therefore take a little longer to complete the backup.