User response to Database Mail
Database Mail in itself can only send emails, because it only 'talks' SMTP:


  A Database Mail account contains the information that SQL Server uses to send e-mail messages to an SMTP server. Each account contains information for one e-mail server.


(from the documentation)

But (depending on the configuration of your SMTP server), you can use a valid email address within your organization (a user, or a group like info@example.com) as the sender of the email. Then, the receiver can just reply as they would to a normal email.

If you need to make some automated actions based on a reply (such as scheduling another task in the database), you're looking at a (much) more complicated integration, way beyond the scope of Database Mail.