There's lots of people who don't know what the phrase mission critical means.
It means: (of hardware or software) vital to the functioning of an organization.
Lots of companies are doing things that are not of vital importance; they don't control an Air Traffic Control system.
But your employer is asking whether you'll treat the their systems as is they are of vital performance. In other words will you make creating quality products important to you, and have you done that before somewhere.
The employer thinks they'll be able to tell in your answer how much you cared about what your previous employers were doing and therefore how you're treat their software and hardware.