Legal liability covers your liability to pay compensation for death or bodily injury to other people or loss or damage to their property resulting from an incident, which happens in connection with you owning or living in the home at the insured address. For instance, if a person was to come onto your property and injure themselves by tripping whilst climbing the stairs, the Home legal liability component of your policy would respond if you were found legally liable for the injury sustained and damages were sought from you.*
Legal liability on contents also covers your liability to pay compensation for an incident, which causes death or bodily injury to other people anywhere in Australia or New Zealand. So if you were playing golf at your local golf club and your ball was to strike another player causing injury, the contents legal liability component of your policy would respond  if you were found legally liable for the injury sustained and damages were sought from you*.
* This example assumes your claim was not otherwise excluded by your policy.