The International Standard Book Number is a 13 characters long unique international identifier associated with each edition, version, or format of your book. If you are a citizen of some countries you purchase it from the appropriate national agency, while in other countries, you get it for free upon request.
Tip #1: If you only publish on Kindle or on your own website, you don't need an ISBN.
Tip #2: Individual vendors may assign proprietary identifiers, such as Amazon ASIN to your book, but these are not international recognized and are only useful within Amazon's system.