According to Django docs:

A boolean. If it’s False, send_mail will raise an smtplib.SMTPException.

So basically, if it's true, you'll get no log or error of a failed sent email.

More info here.

As qouted by @Nifled, fail_silently() will raise an exception from smtplib. I will explain it by quoting an example: Assume your web app sends an email to a user who submits a feedback every time. If fail_silently() is set to False while DEBUG mode is set to False or True you will get a very ugly error page(although useful in the beginner stages) which you might not want to show to your user and hence fail_silently()=True comes to your rescue. Hope now it's clear!!.