What does "full format operation" do to a disk?

A quick format just deletes the allocation table and leaves the files in place.

On the other hand the full format DOES NOT go through the whole partition and erase data ON PRE-VISTA VERSIONS OF WINDOWS. What it does is basically scandisk and quick format. This way if there are any errors on the disk itself, they will be found and bad blocks will be marked as such and possibly replaced by spare blocks by the HDD. This way we can be sure that the formatted partition is physically in good condition and may be used.

Here's a source form Microsoft that backs that claim.

Info for Windows Vista (and I presume 7) Apparently a "full format" in later Windows versions does indeed overwrite each sector.

Full format post-Vista will supposedly zero the drive, ensuring that all data is erased. If the formatting that is done obeys the Microsoft documentation, the data will be completely erased.

A forensic lab equipped with the right equipment can still "peel back" layers of magnetism to peek at older data, even if it was over-written several times. But this should not concern you, unless you are in trouble with some national security agency.

Your disk manufacturer may supply a "low level disk format utility". Nowadays, low-level formatting no longer applies to modern disks, so these utilities just reinitialize the disk to all-zeroes and try to resurrect bad sectors, but I would trust more such a utility to correctly reset the disk than the Windows format utility.