What are the different types of insurance that people commonly have?

I was wanting to know what insurance do people usually have I know that there is car insurance but others I am not sure since I wasn't taught any of this. Please write the common types people have and what it does/covers. I was called the dermatologist to make an appointment and they asked if I had insurance, could someone explain why I would need it, also I believe im under my parent's insurance how does this work. Again what are the common types/ what it covers, and the other two questions.