Arguably, one of the most critical words in christology—the study of the person and work of Christ—is the Greek word monogenēs which has been somewhat misleadingly translated in the past as “only begotten.” The connotations of “only begotten” are ambiguous because the word “begotten” is no longer a part of everyday English and is unfamiliar to modern readers. Furthermore, “begotten” may not be the sense John intended.
The NIV translates monogenēs much more meaningfully as “one and only”, as in John 3:16: “For God so loved the world that he sent his one and only Son . . .” The CEB, NLT, HSCB, and the ESV likewise have “one and only Son”, or simply “only Son”.
The word monogenēs is used only a few times in the New Testament. Luke, and the author of Hebrews, used this word about certain people always to emphasise that the person was an only child. The word is not used to emphasise, or refer to, the “begetting” of these children. See Luke 7:12 (the Widow of Nain’s son); Luke 8:42 (Jairus’ daughter); Luke 9:38 (a boy tormented by an evil spirit) and Hebrews 11:17 (Isaac).
John is the only New Testament author to use monogenēs to describe Jesus. He used the word to highlight the unique relationship between God the Father and Jesus Christ. Like the other New Testament authors, John did not use the word to emphasise, or refer to, “begetting”. (See John 1:14 & 18; 3:16 & 18 and 1 John 4:9.)
Monos means alone or sole; genos has a range of meanings: offspring, family, relation, lineage, race, kind, species, etc. BDAG defines monogenēs as something “that is the only example of its category.”
The real implication of this word is that Jesus Christ is God’s one and only, unique Son. As such, Jesus fully shares divinity with the Father and with the Holy Spirit (Col. 2:9 cf. Heb. 1:3).
Amazingly when we become followers of Jesus we too can share in his glorious inheritance as adopted sons and daughters (Rom. 8:14-17).
 A Greek-English Lexicon of the New Testament and Other Early Christian Literature, 3rd Edition, by Walter Bauer, revised and edited by F.W Danker, 2000. (Known as BDAG for short; an acronym of the four authors who have worked on it: Bauer, Danker, Arndt and Gingrich.)