Meaning and Derivation: Adonai is the verbal parallel to Yahweh and Jehovah. Adonai is plural; the singular is adon. In reference to God the plural Adonai is used. When the singular adon is used, it usually refers to a human lord. Adon is used 215 times to refer to men. Occasionally in Scripture and predominantly in the Psalms, the singular adon is used to refer to God as well (cf. Exd 34:23). To avoid contravening the commandment "Thou shalt not take the name of the LORD thy God in vain" (Exd 20:7), sometimes Adonai was used as a substitute for Yahweh (YHWH). Adonai can be translated literally as, "my lords' " (both plural and possessive). [BlueLetterBible]

This word occurs in the Masoretic text 315 times by the side of the Tetragram YHWH (310 times preceding and five times succeeding it) and 134 times without it. Originally an appellation of God, the word became a definite title, and when the Tetragram became too holy for utterance Adonai was substituted for it, so that, as a rule, the name written YHWH receives the points of Adonai and is read Adonai, except in cases where Adonai precedes or succeeds it in the text, when it is read Elohim. The vowel-signs e, o, a, given to the Tetragrammaton in the written text, therefore, indicate this pronunciation, Aedonai, while the form Jehovah, introduced by a Christian writer about 1520, rests on a misunderstanding. The translation of YHWH by the word Lord in the King James's and in other versions is due to the traditional reading of the Tetragrammaton as Adonai, and this can be traced to the oldest translation of the Bible, the Septuagint. About the pronunciation of the Shem ha-Meforash, the "distinctive name" YHWH, there is no authentic information. In the early period of the Second Temple the Name was still in common use, as may be learned from such proper names as Jehohanan, or from liturgical formulas, such as Halelu-Yah. At the beginning of the Hellenistic era, however, the use of the Name was reserved for the Temple. From Sifre to Num. vi. 27, Mishnah Tamid, vii. 2, and Soṭah, vii. 6 it appears that the priests were allowed to pronounce the Name at the benediction only in the Temple; elsewhere they were obliged to use the appellative name (kinnuy) "Adonai." Philo, too, in referring to it says ("Life of Moses," iii. 11): "The four lettersmay be mentioned or heard only by holy men whose ears and tongues are purified by wisdom, and by no other in any place whatsoever." According to Josephus ("Ant." ii. 12, § 4):

"Moses besought God to impart to him the knowledge of His name and its pronunciation so that he might be able to invoke Him by name at the sacred acts, whereupon God communicated His name, hitherto unknown to any man; and it would be a sin for me to mention it."

Pronunciation of the Name by the Temple priests also gradually fell into disuse. Tosef., Soṭah, xiii. 8, quoted Menaḥot, 109b, and Yoma, 39b, relates that "from the time Simon the Just died [this is the traditional expression for the beginning of the Hellenistic period], the priests refrained from blessing the people with the Name"—in other words, they pronounced it indistinctly, or they mouthed or mumbled it. Thus says Tosef., Ber. vi. 23: Formerly they used to greet each other with the Ineffable Name; when the time of the decline of the study of the Law came, the elders mumbled the Name. Subsequently also the solemn utterance of the Name by the high priest on the Day of Atonement, that ought to have been heard by the priests and the people, according to the Mishnah Yoma, vi. 2, became inaudible or indistinct. [JewishEncyclopedia]

In addition to the more defined study above, I recommend checking out this CBN devotional, as well as one of the many other verses that denotes this Name of God.