This file system is just a table which is called FAT (File Allocation Table) or NTFS (New Technology File System). This table will contain names and addresses of files stored on the disk. In other words, every file that you save, will have its exact location (physical address) on the hard disk. So when you save or place any file in the disk, Windows will create some numbers representing the sectors (very small parts of the disk) in which the file reside then place those numbers in the file system table. Then when you double click to open a certain file, Windows will take the file name then check the table to see the numbers (addresses) of the sectors where the file is located on the hard drive and then it Windows() directs the #head of the hard disk to move to those sectors and read their contents , after that the file opens.
When you delete a file, Windows removes the numbers (the address of the file) from the the file system table. That means , the deleted file is technically there on the hard disk but it’s location is not known. The icon (not the contents) representing the file will be placed in Recycle Bin. The reference of the file is removed from the table but the file itself is there hiding somewhere on the disk. The sectors the file occupies will be marked as free (free space) that’s why other new files can occupy those sectors.
When you use a recovery software, the software will bring the numbers back and put them in the table making the file accessible again. When you delete all files and re-format the disk then you will have “permanently” lost the files because the entire table will be gone. but even after formatting, there are some advanced tools that can #recreate the table with all its contents thus recovering all the data.