Quick format deletes data on the surface
Full format goes through every sector and deletes files
A zero fill deletes all data by overwriting it with zeros
Why is this better?
Because When the HDD writes a file to the disk, it just finds the next available "free sector", and overwrites whatever is there (regardless of whether or not it is a 0 or a 1). Zero fill does this after deleting your files effectively overwriting every possible recoverable piece of data.