Adonay, also called Adonai, is one of the names by which Jews designate God. As such, it is a word of Hebrew origin (ădōnay) that means ‘my Lord’.
Formerly, Jews were forbidden, for reasons of respect, to pronounce the sacred name of God. This name, which was what God himself said to Moses in Exodus (3:14), and that was the one that came to us in the form of the YHVE Tetragrammaton (from which Yahweh has derived), was replaced by the Hebrews by Adonay.
Thus, each time they referred to God, or read his name in the Holy Scriptures (in the Tanach, sacred text of the Jews corresponding to the Old Testament, Adonay appears more than 300 times), instead of saying the divine name, They said Adonay (my Lord), as a respectful way of addressing God.
Recently, the Vatican, through Pope Benedict XVI, arranged that the term Yahweh should be avoided in the Catholic liturgy celebration, as well as in prayers and songs, because this term was never used by the Church until 1970, and calls to reuse the terms Adonay, from Hebrew, and Kyrios, from Greek, which means ‘the Lord’.