Suppose you take hourly backups and you loose data in between backups. You can restore the most recent backup, but you will still miss data... in this article I'll explain how you can use the binlogs to restore what you lost.
I recently encountered a problem where we had accidentally created a new database in the root dataspace. We only found out about this after receiving a lot of out-of-space errors. Here is how we moved it to the proper dbspace.