ISBN stands for International Standard Book Number. It’s a globally accepted standard for identifying books. Your book needs an ISBN if it is to be viable: most retailers require it and it helps people find your book.
Probably the only reason not to have an ISBN is if you aren’t going to sell your book and don’t care if people read it. But if that’s the case, why write or publish it in the first place?
If you go with a traditional publisher, they will provide the ISBN. Easy peasy.
If you self-publish, you need to obtain an ISBN yourself. Though you may be able to buy it from the various organizations that help writers self-publish, all ISBNs originate from Bowker. I suggest going directly to them.
Don’t be shocked, but a single ISBN costs $125, while a block of ten currently runs $275. Each version of your book needs its own ISBN, so you could quickly burn through five: hardcover, paperback, EPUB, MOBI, and PDF.
Some companies that support self-publishing buy ISBNs in bulk and then provide them to clients at a discounted rate. However, before you go that route, carefully investigate the details to make sure you are aware of any limitations. This isn’t to imply there are dangers with this option but simply a warning to check before buying.
There is more to know about ISBNs, but this will get you started.