The underlying idea of Liability insurance is the concept of Social Duty of care. Since negligence in this duty of care may cause bodily harm to another person/property, the person who was negligent ought to compensate the effected person. The compensation may be decided in a Court of law/a system specifically set up for it (Employees' Compensation Commissioner) or by compromise outside Court.
Some liabilities are mandatorily to be insured against & may have defined limits of liability (a factory owner’s liability for safety of his employees, Third party liability of vehicles on public road). Other liabilities like a Doctor’s/a product manufacturer are optional & compensation may be decided by courts.
A person/institution that has been negligent is also expected to be responsible for the financial compensation to the victim of the negligence. This compensation amount - as fixed by law or as decided by a Court - is covered in a liability policy.
The policy also provides for legal expenses incurred in defending the case.
Every individual/professional/organisation whose negligence can result in bodily injury/death/property damage should have a liability cover. So an individual householder, a professional/consultant or manufacturer can opt for a liability policy suitable for their needs.