These emails are something new we're trying out.
As LakeRat mentioned, there is something we run on our shared hosting servers called procwatch. It's a homegrown monitoring utility that helps us ensure users aren't breaking other users sites by consuming too many resources on a server. It allows some flexibility before acting and has a some built-in smarts so that it doesn't do things like kill your shell sessions.
Procwatch looks at processes running on the server and is able to see similar information as you do when you run the top command. It knows the server username, process name, duration, and the amount of memory and CPU it's consuming.
I've sampled a dozen servers today and about 90% of the time, processes are killed because they are consuming too much memory. And 99% of the time the process being killed is PHP.
There are lots of reasons that could increase memory consumption. It could be caused traffic to a site, a WordPress site with a lot of plugins, unoptimized code, hacked sites, many sites running under the same user, etc.
Unfortunately we usually don't even know which site it is causing the problems because many users run more than one site under a user. We also don't yet have a good way to expose this information in your control panel, but it's something we want to do.
In the meantime, we're trying out these emails and offering a free month of VPS hosting for those that want to try it. The offer is a no-pressure approach - you can keep your shared hosting as-is, work on optimize your WordPress site, or try a managed VPS server.
Hopefully that provides a bit of clarity into what these emails are and how we'd like to improve your shared hosting in the future.