The Greek word μονογενής (monogenēs) was used nine times in the New Testament: Luke 7:12; 8:42; 9:38; John 1:14, 18; 3:16, 18; Hebrews 11:17; and I John 4:9. In these verses, this word has been translated to either “one and only” or “only begotten.” In addition, the Greek Septuagint version of the Old Testament utilizes this word numerous times.
We see two general uses of the word in the Bible:
1) Pertaining to a relationship between a mother/father and a child - a family issue where the son or daughter is the only son or daughter.
2) Pertaining to a relationship between the Supreme Being and one of His loving servants. This is a spiritual relationship, to be distinguished between a relationship of physical bodies such as mother and son. Many sectarian translations translate the word to "only begotten" - followed by "son."
Such a translation bears a couple of important questions: Could God be so impotent that He could only have one begotten son? And if so, why do the Scriptures state God as having other "sons" including David and others (assuming the translation of υἱός (huios) to "son")?
Accordingly, many scholars over the centuries have argued that the more appropriate translation for μονογενής ("monogenes") means "priceless and irreplaceable." This was certainly how the Hebrew version of the word was translated in Psalms 22:20 and 35:17.
Furthermore, the Septuagint word meaning “only” or “solitary” is μονοτροπος (see Psalm 68:6). This would differentiate from the word μονογενής used here.
In addition, we can see the use of μονογενής as translated as "unique" or "incomparable" from the Hebrew Wisdom of Solomon (7:22), written in Alexandria around 100 B.C.
We can also understand the true meaning of μονογενής as we see other Greek works. In a Greek poem written by Parmenides in the fifth century B.C., μονογενής was used to describe a being who was "unique" (Frag. 8.3-4). This illustrates the use of the word in historical context.
The word μονογενής is also used in the Septuagint Old Testament to refer to Isaac as supposedly Abraham’s "one and only" son (Heb. 11:17). Yet we know that Abraham did not have only one son. Thus the more appropriate translation of the Greek word μονογενής would most certainly be “unique” or “special.”
We can also see that the word μονογενής cannot mean "only begotten" as in "no one else" when we see that God also described David as being His begotten:
I will proclaim the decree of the LORD :
He said to me, "You are my son;
today I have begotten you.” (Psalm 2:7 NIV)
What did David do to deserve this privilege? Certainly we can see, from the statement "I will proclaim the decree of the LORD," that this assignment is due to David's acting on God's behalf, as he proclaims God's message. This illustrates that David has submitted himself to God, and become God's servant (as the more appropriate translation of the Hebrew word בֵּן (ben) in this context would be "follower," "subject" "representative" or "servant" and not "son.") David has surrendered himself to God, and God has empowered him to be His representative. This process, of becoming God’s loving servant, results in a spiritual re-birth of sorts. This is a person who is deciding to do God's will instead of his own will. This “re-birth” is what is being translated to as “begotten” or “begetting” (from the Hebrew word יָלַד (yalad) meaning, “to bear" or "to bring forth”).
In other words, this is a metaphorical use of the word - describing a spiritual rebirth.
Thus we can see that the application of this word μονογενής (monogenēs) is better describing Jesus as having a unique, special, priceless and irreplaceable relationship with God, one that is born from a decision to do God's will. The sum of these would be described as an intimate and confidential relationship.
Thus we can more appropriately translate the two words together: “μονογενής υἱός” as an "intimate" or "special" follower of God, or “confidential" representative or confidential loving servant of God.