An EORI number is a European customs registration number that is required when sending or receiving shipments that cross in or out of the EU. You can request the EORI number for your company from the customs office in your country.
When you are buying products that cross into or out of the EU an EORI number needs to be set in your account. When an EORI number is required for checkout but it is not set in your account you will see a message alerting you to set it in the cart.
If you do not have an EORI number yet you can request this through the website of your customs office: