It means, “Master, Lord.” The Hebrew Old Testament name Adonai and its Greek New Testament counterpart kurios describe the relationship between master and slave. God owns all his children. Thus, Adonai carries with it a twofold implication:

Robert Lightner describes the nature of the master-slave relationship: In Old Testament times the slave was the absolute possession of his master, having no rights of his own. His chief business was to carry out the wishes of his master. The slave had a relationship and responsibility different from that of the hired servant. The hired servant could quit if he did not like the orders of his master. But not so with the slave. He could do nothing but obey (cf. Gen 24:1–12). (The God of the Bible, p. 116)

Lightner continues:
The slave had no worry of his own. It was the master’s business to provide food, shelter, and the necessities of life. Since the slave is the possession of the master, his needs become the master’s. Obedience is the only condition for this provision. This truth is marvelously displayed in Paul, who was himself a bond slave, when he assured the Philippians that God would supply all their needs (Phil 4:19). Only the obedient slave can expect this from his master. (Ibid., p. 117)

The response of both Samuel in the Old Testament (1 Sam 3:10) and Mary in the New Testament (Luke 1:38) serve as beautiful examples of this master-servant relationship.

The nation Israel, however, had utterly failed in their relationship as observed by the prophet Malachi (Mal 1:6).