The “Glory Be” is far and away the most common Christian prayer after the Our Father and the Hail Mary. This prayer is called a doxology, from the Greek word meaning an expression of glory or praise. Christians usually use it as a way of summing up all their feelings and intentions at the end of some longer prayer. In a sense, the glory of God is the purpose and the content of all our prayers and actions, and so we bring them all together as our act of glorifying God in the Blessed Trinity.
The form of this prayer given in the Catechism of the Catholic Church is the one we teach our children; we use it most often when praying the rosary, at the end of each decade, or set of Hail Marys. When Our Lady prayed the rosary with St Bernadette at Lourdes, this was the only prayer she said aloud (since of course, she would not be saying Hail Marys to herself).