EORI stands for “Economic Operators Registration and Identification number”.
Businesses and people wishing to trade must use the EORI number as an identification number in all customs procedures when exchanging information with Customs administrations.
If based in the EU or UK, as a customer you might not need one when purchasing from these locations. However, if you're purchasing from the USA, you might be required to have an EORI number.
Please consult your Tax Advisor or the legal authorities in your country.