Formatting a drive simply means using an operating system to place a file system on a storage device so that it can be transparently written to and read from.
It is unusual to have to perform a re-format; typical scenarious could involve suspecting there is a virus on the system that cannot be removed, or the storage medium is being prepared for a different operating system. Lastly, it happens in the unfortunate system when a storage device (such as a RAID array) has been corrupted or failed by logical means, and the only way forward is seen as re-formatting the array.
Most modern RAID controllers and NAS boxes run a low-level media check on all drives, and actually perform a full format, effectively zeroing the drive and permanently and irrevocably destroying any data. (This is one of the reasons a format takes so long on these storage devices.)
