Here's an analogy for the non-tech savvy.

File systems used by all computers (like FAT, NTFS, HFS, etc) are like a library. Imagine a library. There's the card catalog and there are the books on different aisles and shelves and so on. The card catalog tells you where in the library to find the book you are looking for but it does not contain any actual data; you have to go retrieve the book (file) to read it. A file system is essentially the card catalog to the files on your drive.

When you "delete" a file from your computer, (basically) what happens under the hood is your operating system goes to the card catalog and removes that file's card but it might leave the book on the shelf. Later, when you save a new file to your computer, the operating system might reuse the same position on the aisle + shelf as that old deleted book, and if it does, it overwrites the deleted book with the new one (and thus you cannot recover the book that used to be there). However, there's a chance a deleted file is still on the shelf, untouched, and a piece of software like in OP scans through the entire library, walking down every aisle and looking at every shelf, looking for "deleted" books that are not listed in the card catalog. Sometimes you can recover them, sometimes you cannot (many variables, mostly time + activity).

The biggest exception to that is modern SSDs (depending on configuration of something called TRIM) delete the book at the same time its reference is removed from the card catalog (for faster write performance) and file recovery is impossible.