If you need to completely delete a recipient record and all of it's associated data:
Search for the recipient by email address via: Navigation > Data > Lists > Search Lists
Open a list they exist on by clicking the list icon.
Once in the list click on the recipient icon to the left of the record.
Once on this page there is a Delete Recipient button in the bottom right corner.
Deleting a Recipient will irrecoverably remove their email address, profile data and list assignments and any message activity related to this recipient will be permanently anonymised.
For this reason you are advised to only do this if you are completely sure you wish to delete them from your database.
It might be that you simply want to remove them from a list.