Most books have an International Standard Book Number - an ISBN. You will find it on the back cover with a barcode, and on one of the front pages, along with the publisher's details and the copyright notice. It used to be 10 digits until 2007 when it increased to 13. The digits are in groups separated by dashes, like this: 978-1-84694-282-2. If you self-publish you will have to decide whether you want your book to have an ISBN, because they're not cheap as you have to buy 10 at a time.
The ISBN is simply a product number, but it identifies your book uniquely, including the version and edition. It is used by publishers, booksellers and libraries for ordering, listing and stock control. Without it, your book cannot be ordered except direct from you, if they know about it and how to contact you. Many bookshops will not sell your book without an ISBN because they can't add it to their stock list.
All ISBNs are entered into bibliographic databases, like BookData Online, which are used to provide information to customers. They also notify bookshops and libraries of new books. So it provides an additional set of marketing tools to help your sales.
The different sections of the ISBN indicate the national, geographic or language group, the publisher, and the version or edition (like print, ebook, hardback, paperback, or when you update it). When you buy a block of ISBNs from Nielsen, the agency for the UK and Ireland, the publisher is registered on their database as well as the details of the first book. This means that although people say that you can sell on your spare numbers, the books they are used on will have you listed as the publisher.
The publisher is defined as the person or business who takes the financial risk in publishing the book. If you self-publish, that's you, but if you want your book to look more professional, make up a business name and use that. It doesn't have to be registered as a company, just make sure there isn't a publisher with the same name. So for my book Alina: The White Lady of Oystermouth, my publisher is Alina Publishing. If I end up self-publishing my science fiction (although I hope a publisher will buy it), I can use my other ISBNs and Alina Publishing for them too.