Public liability insurance usually covers you when you are being held responsible to a person or property, as the owner or occupier of your home. For example, buildings insurance usually covers you as the owner of the home for claims such as a tile falling off of your roof and injuring a visitor.
Contents insurance covers you and your family as the occupiers of the property and would usually cover for things like a visitor tripping up over a loose rug. Under contents insurance, you may be covered for personal liability for claims such as you accidentally poking someone in the eye with your umbrella.
For full terms and exclusions please refer to your document of insurance.