First of all, no user can do a "low-level format" in the traditional sense of actually writing to the disk the fundamental tracks and sector boundary markers. That is done in the HDD factory. You CAN do a DOS or Windows Format operation, either Quick or Full, using Windows' tools. What these really do is simply to establish the root directory with no entries, and the files containing data tracking the allocation of "allocation units" (groups of sectors) to specific files. Again, with a new Format operation, the allocation tracking table is written as blank - no units in use. The result is that you cannot get access to any older files already on the drive, even though they exist, because all records of where they are have been overwritten with blanks. So, you have lost all your stuff. If you plan to do this, you MUST back up your data first. (Yeah, I know about file recovery software, and it works, but almost never gets ALL of your stuff back.)
The Full Format operation does a Quick Format like that, and then does a complete test of every sector on the disk to verify that it works. If it does not, this operation marks that allocation unit as unusable so nothing will be put there. When a Full format is finished, you are reasonably assured that all allocation units that are available to use actually will work - at least, until something else fouls one up.
If you want the complete testing process done without losing all your data, that is what the CHKDSK utility is for. You can run it on a disk and it will do the same complete test, but it does NOT do the Quick Format first that removes all file records. It does mark any faulty allocation unit for no further use, and substitutes in its place a different good unit. It cannot recover the data that was in the bad area, so the file that was using that unit now has a big hole full of odd data (or zeros) that means it is corrupted. But you can delete that file (or even try to recover most of its contents first) and still have everything else on your disk.
In behind all of this OS function, modern hard disks constantly are doing their own invisible work. When a disk is first made it has many more sectors and allocation units than it needs for the stated capacity. The extras are set aside as a pool of spares. As the disk is used the controller board on the HDD itself actually does the translation / assignment of "allocation units" that Windows deals with into physical locations on the disks in terms of the old Cylinder, Head and Sector co-ordinates from long ago. As it works it also runs a bunch of self-diagnostic tests, including checking the quality of the signals being read off the sectors. When it detects some weakness it labels that sector a potential problem and moves its reference to its own "Do Not Use" list and substitutes one of its spares. Then it copies the data from the suspect sector to the new substitute, so you don't loose that data. It keeps track of this because, at some point as this is done repeatedly, it starts to run out of spare sectors to use. Then, through the S.M.A.R.T. system, it sends out a warning that it is short of substitute sectors and may not be able to keep you out of trouble much longer. That's when you replace the disk quick, while it's still working!
Now, all this hidden activity by the hard disk unit handles slow random degradation OK because it has time to detect poor-quality signals before they fail completely. But a sudden disaster (for example, a head crash) may produce a problem it cannot fix without data loss; in these cases Windows still will find that a file that uses this area contains corrupted data.
Sometimes the disk's own monitoring system fails to find and fix one or two such errors on its own. However, usually the disk manufacturer's diagnostic utilities will force the disk to go through its entire surface and check for these errors, completely updating itself and making substitutions, etc. If this process is successful and saves all the data in suspect areas, all the data the disk hands over to Windows will be error-free. If it could not save all data, Windows might still find it has corrupted files and CHKDSK can reorganize things, sometimes ending up with a few files that are corrupted so they must be deleted or recovered partially. The combination of these operations may be able to get your disk back into clean operations, possibly missing only a few old files.
However, as croc and mikey5802 have said already, you have to worry why those errors happened anyway, and why the secret automatic background work of the hard drive was unable to take care of them. It is good advice to back up ALL of that disk as quickly as possible, then replace it. Not knowing the original cause, you have to worry that it could get worse fast, and destroy some critical disk area so that you can't get access to ANY of the disk's valuable data.
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