This is what happens in code (
https://github.com/goatpig/BitcoinArmory/blob/master/qtdialogs.py#L4154):
LOGINFO('***Completely deleting wallet')
os.remove(thepath)
os.remove(thepathBackup)
self.main.removeWalletFromApplication(wltID)
self.main.statusBar().showMessage( \
self.tr('Wallet %1 was deleted!').arg(wltID), 10000)
It asks the operating system to delete the file on disk (and its backup). This is a soft deletion. From the perspective of the OS, it will mark the relevant sectors as unused on disk and the data will remain there until the sectors are reused.
With SSDs, since they spread data across cells to increase IO speeds, they also have a built in garbage collector that actively reclaims unused sectors, meaning the likelyhood someone will be able to recover the files months from now if the SSD sees usage is very small (even if it's far from maxing its storage capacity).
For a HDD, it's the opposite. You could likely recover the files years in the future if you didn't actively try to wipe the data.
The newer code makes a point of writing jibberish in the sectors before deleting the file in an attempt to make the data irretrievable. There is no guarantee this works across all OS and hardware. If you want a guarantee your data is wiped, you can use dedicated software to that avail.
