An all or nothing order (AON order) must be entirely filled or not at all. Unlike a fill or kill order, an AON order is not cancelled if not immediately filled. Assuming market mechanisms allow, an AON limit order may remain on the order book until it can be matched in full.
The motivation for using AON orders is obvious: you do not end up with a small block of securities that is not worth the overhead of holding or selling. This may well happen with a simple limit order which matches with a smaller order. It is less likely with market orders unless the order is so large that it cannot match against the order book.