Data wiping is removing data from storage media before the media is disposed of, reused, or otherwise removed from its current production use. Secure data wiping is an enhanced version of removing data from the media. Secure data wiping usually requires overwriting of the entire disk with specified patterns to ensure that the original data is not recoverable.
Failure to securely wipe data from storage media before reuse or disposal, can allow data to be recovered by a third party. Disposal of storage media may involve destruction of the media, resale of the media, or sending the device to a recycler who then has control over the media. Any of these options, except for on-site media destruction, means loss of control of the media and the third party could attempt to recover the data from the media.
Organizations expect that all storage media will be overwritten with multiple passes of data designed to make the data unrecoverable. There are multiple standards for these patterns and number of times; and the standard followed should be named, or the details of any custom solution should be specified in the answer. They would also look for any media that cannot be securely wiped should be destroyed.