In connection with papal infallibility, the Latin phrase ex cathedra (literally, "from the chair") has been defined as meaning "when, in the exercise of his office as shepherd and teacher of all Christians, in virtue of his supreme apostolic authority, (the Bishop of Rome) defines a doctrine concerning faith or morals to be held by the whole Church".
The "chair" referred to is not a literal chair, but refers metaphorically to the pope's position, or office, as the official teacher of Catholic doctrine: the chair was the symbol of the teacher in the ancient world—the post of university professor is still referred to as "the chair"—and bishops to this day have a cathedra, a seat or throne, as a symbol of their teaching and governing authority. The pope is said to occupy the "chair of Peter", as Catholics hold that among the apostles Peter had a special role as the preserver of unity, so the pope as successor of Peter holds the role of spokesman for the whole church among the bishops, the successors as a group of the apostles. (Also see Holy See and sede vacante: both terms evoke this seat or throne.)
The response demanded from believers has been characterized as "assent" in the case of ex cathedra declarations of the popes and "due respect" with regard to their other declarations.
Read more about this topic: Papal Infallibility