What is an EIN? It is the US Tax ID that everyone, companies and individual authors alike, must have when publishing a book to one of the main eBook retailers, like Amazon/Kindle, Apple/iBookstore, Barnes&Nobel/Nook etc.
Why is it necessary? Because all of these retailers are US based, so they are obliged to submit earnings statements to the IRS. If you are in the USA or a US citizen, you need to declare your US taxes on book sales, just like any other income stream (as an individual you probably have a TNI). If you not in the US and you are not a US citizen, then you need to submit a tax waiver form, called the W-9 Form. For that, you need the EIN.
The service is free and getting one is normally done by filling in a form (Form SS4) and sending it off by post or fax. You can also request the EIN by phone, but it still takes some days for the certificate to arrive by post and for them to update their database.
Amazon/Kindle lets you worry about your tax liabilities, while Apple requires you have the EIN in hand and registered before they will let you publish books to their iTunes bookstore.