Today, the new Single European Payments area is officially in force.
Based on the cooperation of European banks, the system provides a new way to make credit and debit payments (thus, including bank transfers) to any European country under the same conditions applicable to domestic payments. This should both enhance safety and decrease operation time.
In practice, this implies that the costs of making a transfer/payment to another SEPA-state (34 of them so far) should not exceed those charged for "internal" transfers. You should also be able to use your bank card to make payments abroad.
On the other side, if your system so far allowed you to make national transfers using only the receiver's bank account number (that is, without IBAN), that will no longer be possible.
More info? Take a look here!