A strategic picnic, as the Soviet empire was, led to this concordat with the Sovereign Order of Malta (SMOM), a religious order placed directly under the pope. It regulates the largest social service provider in Hungary, the Hungarian Malteser Charity Service. (Magyar Máltai Szeretetszolgálat or MMSZ). This agreement is one of more than 70 “treaties” with various countries which put their social services under Vatican control.
With this tiny concordat, Hungary became the second Warsaw Pact country (after Poland did so on 17 July 1989) to establish diplomatic relations with the Vatican. It states that Church-related issues are to be settled in accordance with both Canon (Church) Law and Hungary's new law on religious freedom. It replaces a pact with the Communist regime which is still being held secret. 
This concordat was the best financial package that the Vatican could get from the Socialist government. In fact later, when Hungary ran into financial difficulties, the payments to the Vatican became a hardship. However, four years later the conservative government amended this concordat to give the Vatican an even better deal.
Stonewalled by the Vatican, Hungary learned in 2006 that concordat negotiations cannot be re-opened — unless the Church thinks it can get a better deal. Otherwise it's in the Vatican's interest to simply stall until a more favourable political climate ends the opposition to it. In 2010 this is what finally happened.
After 16 years and a change of government the Vatican was able to renegotiate the Hungarian financial concordat to get even more favourable terms. Naturally, the public was unaware of what was going on.