A concordat is an agreement between the Church and a secular power. One could say they concern religious matters, but the concerns of religion have had a wide scope over history. There have been many concordats over the years.
One of the most contested issues defined by concordats has been the authority over the selection and appointment of bishops. Who appointed bishops? Pope or king? Until recent times, bishops had much greater secular power than they have today, so it was an important issue for both sides.
The most recent example of a concordat is the Concordat of Portugal signed between the government of Portugal and the Holy See in 2004.
In Prolog of The Templar Concordat, the agreement between the pope and ther Templars is the Concordat of Nocera. It is this same concordat that defines the relations between the two in the present day.