If you use Time Machine for backing up your stuff, and if you have a disaster requiring the full recovery of everything from your Time Machine Backup, here is what you would need to do:
1. Assuming your Mac has been running Lion (OS 10.7) or beyond, you would first boot to the Recovery HD partition on your internal drive (this link talks about that partition: how to boot to it, and what it can do:
https://support.apple.com/en-us/HT201314).
2. Next, you have a choice:
A. If the drive is OK, you can choose the first option to perform a complete recovery from the Time Machine backup. Once that is done, you can then boot your Mac "like normal".
B. If the drive is damaged. you would use Disk Utility to Erase, Format, and if necessary, Partition the internal drive. Then, you would do a clean, "virgin" installation of whatever OS you had been using. Finally, you would then boot your Mac, and then use Migration Assistant to "migrate"/copy all the "necessary" stuff from the Time Machine backup.
Now, the other way of backing up/cloning one's Mac is to use either SuperDuper! or Carbon Copy Cloner. If you then have a disaster requiring the full recovery from the SuperDuper! or Carbon Copy Cloner backup, you would boot your Mac from such a backup (ie, not use the Recovery partition). From there, the options are "similar". That is, if the drive is OK, you would perform a "Restore all files" (that's the option in SuperDuper!, which is what I use. Carbon Copy cloner has something similar, but I do not know what it is called). What SuperDuper! does in that case is to Erase the internal drive, and restore everything from the backup to the internal drive. Then, one would just boot their Mac normally, and be back in business.
If the drive is bad, then one would use Disk Utility on the backup to Erase, Format, and if necessary, partition the internal drive, do a virgin installation of the OS one had been using (it would be necessary to have the "Install OS X "whatever"" file on the backup; I of course have mine in two places). Then, boot your Mac, and like above, use Migration Assistant to "migrate"/copy all the necessary stuff from the SuperDuper! (or Carbon Copy Cloner) backup.
You are probably thinking that both processes basically function the same. Yes, that is true, but the huge advantage of a clone/backup is that one can actually do their work running from the backup (albeit slower). And, the other big advantage is that if the internal drive on your Mac is beyond repair, one can still work via the backup until a new drive is installed. In such a case, one would not be able to boot to the Recovery HD partition. That is another reason why it is imperative to perform disk cleanup/maintenance/repairs on a periodic basis. Disk Utility is "OK" for such tasks, along with Onyx and one's own cleanup efforts. But, I prefer TechTool Pro (along with Onyx) instead of Disk Utility for my weekly disk maintenance/repair tasks. It can perform some functions that will warn me when the drive is starting to go bad.
Finally, there are instances where the Recovery HD partition does not get created from an OS installation. I believe such instances are rare, and I have never had an issue with it. But, I have seen it mentioned on some other sites/discussion groups.