In a nutshell, accidental damage is damage to your home as a result of a non-deliberate act (or in the case of the puppies, a deliberate but innocent act!).
You won't be insured against general wear and tear around your house. For example, if your sofa wears thin and tears or your television stops working. To make a claim, something needs to have happened to the item in question – it won't be covered if it simply wears out or fails for no reason.