There are cases that you need to have an immediate notification for super important messages.
For example a water issue that could create a serious damage need a different way of notification.
The problem: iPhone in mute does not allow sound to almost any application (e.g. telegram)
The solution: sms and tts voice phone call using ClickSend service. You could configure iPhone to bypass the mute per sms/phone call.
See more detail https://github.com/hhaim/hass/wiki and
and example
Just as a heads up, the iOS HA app v2 (currently in beta) will have the ability to receive critical alerts as well - I’d probably stick with their native implementation over a 3rd party, but this is certainly a good option for Android devices!
I am not sure how many service providers still provide it, however, e-mail to sms is an option for some and is free.
Sprint in the U.S. for example will send a text using [email protected] if your phone number was 123-456-789.
I’ve googled that Apple guys do not allow for almost any application to override the silent mode (only medial apps)
Any of the notification apps (e.g. pushbullet, Telegram) does not have this option so it is realy surprising that IOS HA v2 was able to get it …
I hear you, no idea what limitations or requirements are needed to allow this but they do have it listed here: Home Assistant for iOS 2.0 Beta Testing
“Critical events” could mean anything.
I would be surprised if it is working like I would interpret it 
It is working like you imagine, I’ve been using it for months now ever since the beta introduced it. Critical alerts ignore any silent mode / night mode / sound level settings in iOS and play at the configured volume. Custom sounds can be used too and the beta allows importing and using all iOS system bundled sounds as well.
What version of the iOs app is needed for the critical alerts?
@olbjan could you explain how there is not even one notification application that was approved by Apple for critical messages. We are talking about big companies (Telegram, Pushbullet etc) that all their business model is notifications while iOS2 beta was approved
Something does not make sense here …
That’s pretty simple: Those are messengers, not apps for critical notifications.
Apple requires use cases that warrant bypassing their controls such as danger to personal safety or property. It took Robbie three months to successfully prove Home Assistant has valid use cases to use critical notifications and there are only a handful of other applications right now that have the same functionality, mostly around severe weather warnings for example.
@olbjan Interesting. This is a killer feature. as you said only handful applications (e.g. medial) could use this critical message capability. It can only be explained if those guys at Apple are using HA 
The key thing from what @olbjan said which sets HA for iOS apart is that Apple only approves critical notifications for very certain application types, namely life safety (e.g. continuous glucose monitors for diabetics), healthcare, public safety and personal safety/security apps. You will never see Telegram, WhatsApp, FBM, etc, supporting critical notifications since they don’t fall under one of the approved categories. I’m very proud to have received this special permission from Apple, as it does set Home Assistant Companion for iOS above all others, including Apple’s own official Home app.
You can find more information about critical notifications here.