Tax Identification Number (TIN)
Many countries use Tax Identification Numbers (TINs) to identify taxpayers and facilitate the administration of their national tax affairs. TINs are also useful for identifying taxpayers who invest in other countries and are more reliable than other identifiers such as name and address.
In the US, a TIN may be assigned by the Social Security Administration or by the Internal Revenue Service (IRS).
In the EU, TIN specifications (structure, syntax, etc.) are set by the national authorities. Some countries even have a different TIN structure for different categories of individuals (e.g. nationals and foreign residents). Check this page from the European Commission for more information. A TIN is not a VAT number.