1) What is the Assumption of Mary?
The Assumption of Mary is the teaching that: The Immaculate Mother of God, the ever Virgin Mary, having completed the course of her earthly life, was assumed body and soul into heavenly glory [Pius XII, Munificentissimus Deus 44].

2) What level of authority does this teaching have?
This teaching was infallibly defined by Pope Pius XII on Nov. 1, 1950 in the bull Munificentissimus Deus (Latin, “Most Bountiful God”). As Pius XII explained, this is “a divinely revealed dogma” (ibid.).

This means that it is a dogma in the proper sense. It is thus a matter of faith that has been divinely revealed by God and that has been infallibly proposed by the Magisterium of the Church as such.

3) Does that mean it is an “ex cathedra” statement and that we have to believe it?
Yes. Since it is a dogma defined by the pope (rather than by an ecumenical council, for example), it is also an “ex cathedra” statement (one delivered “from the chair” of Peter).

Because it is infallibly defined, it calls for the definitive assent of the faithful. Pope John Paul II explained: The definition of the dogma, in conformity with the universal faith of the People of God, definitively excludes every doubt and calls for the express assent of all Christians [General Audience, July 2, 1997].

Note that all infallibly defined teachings are things we are obliged to believe, even if they aren’t defined “ex cathedra” (by the pope acting on his own).

The bishops of the world teaching in union with the pope (either in an ecumenical council or otherwise) can also infallibly define matters, but these aren’t called “ex cathedra” since that term refers specifically to the exercise of the pope’s authority as the successor of St. Peter. (It’s Peter’s cathedra or “chair” that symbolizes the pope’s authority.)