Critical Alerts override the Do Not Disturb feature if you have it enabled on your iPhone or iPad, and will even arrive with an audio alert when your device is muted.
The idea behind Critical Alerts is that if specific apps have crucial information that shouldn’t be ignored – notifications related to health, home security, or public safety, for example, then you’ll be alerted regardless of your other device settings.
The Critical Alerts feature is going to have limited use, you’d only want appropriate apps to have access to it (think glucose monitoring or weather warning apps) which is why Apple requires that developers apply for an entitlement to support them.