They are something new we've started trying around the middle of this year.
For a little background, "procwatch" is a service that runs on all shared hosting servers that tries to ensure fair usage of its CPU and memory resources. It has some intelligence built into it instead of just blindly killing processes that exceed some set limit. That means sites can get a little more resources for small spikes in traffic when the server isn't overly busy and we don't kick you out of your SSH sessions. If it does kill a running process, it usually means that something temporarily stops on your site. It could be a valid page request, a long-running upload, or in most cases, a WordPress plugin or theme that becomes a memory hog. (I can't stress enough how much caching helps a WordPress site!)
In the past, when customers have bumped into the limits of their shared hosting account and the server didn't have anymore to give, procwatch would dutifully kill the process and the site owner usually never notices. We're using these emails as a way to let customers know this is happening so they can take action if they want to.
The bad news is that it's very hard to diagnose the problem programatically. It takes the site owner, and/or our Tech Support team, to look at the site and logs to determine why it's using a lot of CPU or memory. Sometimes it's fixed with a simple config change, enabling caching, or upgrading to a VPS to have more memory. If you think the latter may be best, we're offering a free month of VPS service so you can try it risk free.
We're still working on the emails to provide better information. Right now procwatch only reports the server user that is running the process that was killed (because users own processes in linux). The next iteration should report the website(s) that user owns and we can include that in the email. Depending on how useful these messages are, we'd like to add these as notifications in the control panel instead of emails.
We'll keep refining the messages to provide better information. Please let me know if there's any changes you'd like to see and we can try testing that too.
Hopefully that helps provide some context around these emails and what we're trying to accomplish. It's all about providing you with more information about your website and making sure you're using the best hosting option for it.