The International Standard Book Number (ISBN) is a 13-digit code which is used to uniquely identify a book. This number allows publishers, libraries, and book dealers to locate books. Books with an ISBN will appear in Bowkers Books in Print which is what booksellers use to locate the publisher of a book so they can order it. If you wish to sell your book through retail outlets you must have an ISBN for it.
The 13-digit number is broken down into sections separated by a hyphen. For example an ISBN may look like this: 978-0-9768076-7-4. The sections identify different things, one of which is the publisher of the book. You will often see ISBNs printed without the hyphens. Starting Jan 2005 the book industry started to adapted a new 13 digit ISBN system, before that time ISBNs consisted of 10 digits.
In the United States ISBNs are assigned by R.R. Bowker through the website Identifier Services. They are the only authorized seller of ISBNs in the USA. You may purchase a block of ISBNs or a single ISBN. If you have more than one book you will be publishing purchasing them in a block is more cost efficient.
Some companies offer to resell you a single ISBN but this is a violation of the ISBN standard and of industry practice. Subsidy or vanity publishers will offer you an ISBN for your book. Be aware that the ISBN they assign to your book identifies them as the publisher of the book, not you, and you will not be able to use that ISBN if you take your book to a different publisher or self-publish. In order to be a true self-publisher you must purchase your own ISBN.