It stands for Federal Employer Identification Number and it is issued by the IRS. Most business entities, including, Limited Liability Companies, Sole Proprietorships, Corporations or Partnerships are required to have a FEIN. There is an exception if you are sole proprietor without any employees, in which case you can use your social security number.
You can get a FEIN on the web immediately by filling out & filing Form SS-4, the Application for Employer Identification Number. You can also apply over the phone and receive it the same day, but you should review the application and gather all the information required before calling so that you have all the answers you need. If you file the form by mail or fax, it will take longer.