This will be caused by no email address being defined in the user's email settings.
To add an email to the user:
On the System tab, click User Profiles
Select the user with the issue.
Click E-mail
In the Email field, enter their email address, if required set an email name and CC address.
Make sure that an SMTP User and SMTP Server have been set, usually there's just 1 option to choose from. Refer to a working user if necessary
Click Save.
Ask the user to log out and back in again and then attempt to email again.