That looks like HTML from the User menu. I would recommend a couple of things:
- Enable DEVELOPER debug mode. You can do this by going to Site Administration > Development. While you are there, be sure to check the box right below it to display errors. I suspect you may find that your site is generating errors that are hidden most of the time.
- Switch to the Boost theme.
- Check the HTML for error (view source), notice and warning medsages as some of these may not necessarily visible when a page is displayed.
- Once you have fixed any errors, try the test again.
Take a look at the README.md file included with the eMailTest plugin - also available from the Additional Documentation link on the plugins page on Moodle.org. It includes some troubleshooting tips.
What version of Moodle are you using?