From a profile page, find the purple "Actions" button and click "Delete profile".
You'll need to either set up or input your security pin to proceed.
If you are deleting what appears to be a duplicate file, do this quick check to make sure it's not actually a duplicate:
Check the phone numbers, emails, and addresses on the account and make sure there is only one preferred for each. (Spouses can have their own preferred phones or emails.) If there are two preferred of any of those items, it can cause duplicate entries when you run reports.