Machine Check Events
A machine check exception (MCE) refers to faults that the processor can detect and signal to the OS.
Which will frequently be about faulty hardware.
Whether it's a warning or error varies.
For entirely practical reasons you may see more warnings,
if only because for various errors it may be a good idea to halt a still-running system,
which will be just before they might get logged, and well before they are subsequently viewed by you.
You're probably here because you saw syslog entries like:
[Hardware Error]: Machine check events logged
For more detail, look at things like the mcelog package, and its logfile, e.g. /var/log/mcelog
These are often warnings, but often also warnings you want to know about.
For example, in my case the CPU was being throttled because it was overheating (~90C).
See also:
http://www.mcelog.org/faq.html