The only official currency in Hungary is the Forint. (HUF). Euros are accepted at most places, but it is better to change at the exchange offices since the exchange rate is notably lower.
It is advisable to get Hungarian Forints upon arrival than exchanging them with a bank at home as local Hungarian banks and currency exchange offices work with much better rates.
DO NOT exchange money at the airport in Budapest since the exchange rate is notably worse. The currency exchange offices are reliable.