insurance

My school has always carried accident and liability insurance protection through the AAU. Recently one of the municipalities I teach in has informed me that the AAU coverage carried is not adequate to teach at their location. I was curious, if you teach out of a rec center, church, community...

I hear about schools having insurance. Is this an insurance to protect from lawsuits if someone gets hurt or is to cover medical expenses in case someone gets hurt? Do schools want someone to use it if they genuinely get hurt? What should I know as a student in case this does happen?