Most of us realize that merely deleting a file doesn't really remove it from the hard drive or other storage media it resides on. (For some background on this issue see a post I wrote a while back.)
Given how we use digital devices today – both for work and personal use – we can't just abandon this issue to our firm IT staff. Our personal computers at home, our phones, copiers, memory sticks and ipads all probably contain our own personal information, or personal or confidential information of others. We need to manage that not only while we use those tools – but when we dispose of them as well. Pulverizing them into dust – aka destruction to the smithereens level – is not always an option.
This Microsoft article is worth a read, as it explains the issue, has some suggestions to reduce the risks, and links to some disk erasing tools.