Statutory financial statements are those that a business is required to prepare by law. This basically comes down to their annual accounts, which companies must prepare in a format specified by law and accounting standards, file with whichever government body they must be filed with, and give to all their shareholders. As a public document, companies will usually give these away free or for a small charge to anyone else, too.
Non-statutory financial statements would be anything else. A well-run company should, for example, be preparing management accounts at least once a month to keep the board informed of how well things are going. If they show that things are not going well, then the accounts could give some clues as to why and help the board decide what to do about it.