IBAN stands for International Bank Account Number, which is an international banking system for bank account numbers. IBAN makes international transactions easier in many countries.
As opposed to a BIC code, which refers to a specific bank, IBAN refers to a specific bank account.
IBAN is used in all European countries (except Russia and Belarus) and dozen of non-European countries. Inside the European SEPA zone zone it's very convenient to transfer money to other countries.