Error #-200: HTTP Error.

While attempting to upload a sermon from the front-end of our recently-upgraded Joomla! site, I got this message about half-way through the upload:

Error #-200: HTTP Error.

Can you enable error reporting (set it to max or development) and check if any errors appear either on the site or in the error log (ask you hoster if you don't have access to them).

Also check if that happens also with smaller files.

I apologize for being a bit too much of an amateur to understand the directions to "enable error reporting (set it to max or development)."

If I contact the customer support for our website hosting service, what specific question could I ask? For what part of the website am I asking for "error reporting"?

"Error Reporting" is a setting in your Joomla Configuration. "Maximum" or "Development" are options you can select in that parameter.
After you have that enabled, Joomla would show PHP errors in your browser when they happen. That may help find some issues. Even if they don't show up, they should at least get logged in the PHP error log file.

When asking your hoster, it's best to give them the exact time when you tried the upload(s), so they know where to look. Ask them if they can see any errors regarding that upload. It may be a PHP error or some other stuff done on the server (eg antivirus protection or security rules and the like). They usually know better where to look than we do