Public Liability Insurance covers any awards of damages given to a member of the public because of an injury or damage to their property caused by you or your business.
In other words, if you or your business injures a third party (that doesn't mean someone who works for you, they're covered by Employer's Liability), or their property, PL insurance provides financial protection against damages that might be awarded in a lawsuit (and, depending on your policy, legal fees etc).
Definition source: Crown Copyright