Adding to a task list - User does not exist or is not unique

We have SharePoint 2010 with a single web server front end and another server as the SQL server.  When trying to add a task to a list or an announcement to a page, users are getting the error, "The user does not exist or is not unique."

I have searched diligently for an answer, but cannot find anything about this with regards to users getting the error. 

Thank you in advance for your assistance.