What does the emergency dialer let you do?
You can only dial emergency numbers, which vary by country/region (911 in the US; certain countries such as France have multiple emergency numbers). Dialing regular numbers produces the following error:

 

Starting with iOS 8, you may also dial emergency contacts by opening your Medical ID. Interestingly, as of iOS 9.3.4, if you have one of those numbers memorized, you cannot punch it in directly. You must go through the Medical ID to ring it up.