Problems with sending email to Jenkins localhost

I'm learning the nuts and bolts of using the Jenkins automated server at work for our DevOps tasks. Currently, users can't send request emails to localhost unless they log in as localhost-- essentially, they have to send an email to themselves when logged in as localhost, or else the email will bounce back. What is a better way to configure this mail client?

(Caveat: I didn't set up the email client, but I'm trying to learn more about Jenkins so I can do a better job with it than the employee who was previously in charge of it.)

I'm all ears to any advice that's offered!