A good way to think of it is as a library. We have a set of index cards (the file table) relating to the books (files) on a shelves (clusters). If you need a file, you look up the index, go to the right place and get it. When a file is 'deleted' the index of the cluster is marked as 'deleted' but the actual file is still there. When the 'shelf' is full, the system looks at the file table, finds a location thats marked as deleted and overwrites it. This saves on writes. The actual file, or parts of it is not overwritten till the space is needed - which makes it recoverable.
The computer ignores 'deleted' files when calculating space since, well, as far as its concerned, there's nothing important there.
A 'secure' deletion is simply overwriting the area with zeros or random information.