What is a private liability insurance?
This insurance pays for the damages you caused and you are liable for.
In the first examples these are the costs for the new car paint.
The liability insurance also helps when someone demands a compensation for damage from you without a reason. This is called legal protection.
In the second example the owner of the smartphone wants a compensation. The insurance helps you to defend against this claim. The insurance takes care of the letters. The insurance also pays for a lawyer, if you need one.
Third example:
You walk over the street. You don´t take a look around. A bus evades. The bus spins out of control and crashes into a tree. Many people are injured. The bus cannot be repaired. Without a private liability insurance you would have to compensate the whole damage on your own. This can be very expensive. In the worst case you pay the rest of your life for it.
Who is insured?
In a family liability insurance the whole family is insured. Children are insured in the family liability insurance until the end of their first apprenticeship.
In the single liability insurance adults can insure themselves alone. You are single, when you are not married.