Formatting Vs. Deleting

What is the difference between formatting something (e.g a flash drive) and just deleting the files?

A full format overwrites not only the directory structure (the FAT) but also the sectors where the file(s) reside on the platters. An analogy for this is writing information on a blackboard with a piece of chalk. When you "delete" it you erase it, it's gone for good and can't be recovered.

Deleting a file in modern OSes just deletes the entry in the FAT or whatever the file system uses for such purposes. An analogy for this is taking a book and deleting or simply blacking out the entry for chapter 13 in the Table Of Contents - while the TOC now doesn't have a chapter 13 listed, the actual chapter in the book is still there.

Unless of course you go the extra step to "delete" the pages in the book by ripping them out.