υἱός (huios)

The Greek word υἱός (huios) has been used variously throughout the New Testament. There have been various uses of the word - see below.

According to Strong's lexicon, the word can mean "son" - but only "in a restricted sense, the male offspring (one born by a father and of a mother)." This means a biological son. But according to Thayer's lexicon, the word υἱός (huios) can also mean:
"used to describe one who depends on another or is his follower - of teachers - i.q. pupils."
Thayer further describes the meaning of this word in other contexts:
"one who is connected with or belongs to a thing by any kind of close relationship."
And further:
"instructed in evangelical truth and devotedly obedient to it"
"one to whom anything belongs"
"those to whom the prophetic and covenant promises belong"
"The Jews called the Messiah υἱὸς εἶ τοῦ θεοῦ pre-eminently, as the supreme representative of God"
Terms that would appropriately describe such a relationship described above using the Greek word υἱός (huios) would thus be:
- follower
- devotee
- subject
- servant
- representative

The later use, as representative, is also consistent with the follower or devotee performing their service activity on behalf of the one they follow - as Jesus was acting on behalf of God. Jesus confirmed his position as God's representative throughout his teachings, with statements such as:
“Anyone who welcomes you welcomes me, and anyone who welcomes me welcomes the One who sent me." (Matt. 10:40 NIV)
“Whoever listens to you listens to me; whoever rejects you rejects me; but whoever rejects me rejects Him who sent me.” (Luke 10:16 NIV)
"And the Father who sent me has himself testified concerning me. (John 5:37 NIV)
"For I have come down from heaven not to do my will but to do the will of Him who sent me. (John 6:38 NIV)
"And this is the will of Him who sent me..." (John 6:39 NIV)
“No one can come to me unless the Father who sent me draws them... (John 6:44 NIV)
"Just as the living Father sent me and I live because of the Father, so the one who feeds on me will live because of me." (John 6:57 NIV)
“My teaching is not my own. It comes from the One who sent me." (John 7:16 NIV)
"I am one who testifies for myself; my other witness is the Father, who sent me.” (John 8:18 NIV)
In these statements and many others, Jesus is not only describing himself as God's servant: He is also describing his position as being sent by God - and thus acting on behalf of God. Such a position would appropriately be described as God's representative.

Further to this point of the use of the Greek word υἱός (huios) - consider other uses of this word υἱός (huios) among Jesus' statements in the Bible (NIV):
"But the subjects [υἱός (huios)] of the kingdom will be thrown outside, into the darkness, where there will be weeping and gnashing of teeth.” (Matthew 8:12)
"The field is the world, and the good seed stands for the people [υἱός (huios)] of the kingdom." (Matt. 13:38)
“Say to Daughter [υἱός (huios)] Zion, ‘See, your king comes to you, gentle and riding on a donkey, and on a colt, the foal of a donkey.’ ” (Matt. 21:5)
“Woe to you, teachers of the law and Pharisees, you hypocrites! You travel over land and sea to win a single convert, and when you have succeeded, you make them twice as much a child [υἱός (huios)] of hell as you are." (Matt. 23:15)
“How can the guests [υἱός (huios)] of the bridegroom fast while he is with them? They cannot, so long as they have him with them." (Mark 2:19)
"Truly I tell you, people [υἱός (huios)] can be forgiven all their sins and every slander they utter" (Mark 3:28)
"But love your enemies, do good to them, and lend to them without expecting to get anything back. Then your reward will be great, and you will be children [υἱός (huios)] of the Most High, because he is kind to the ungrateful and wicked." (Luke 6:35)
"Now if I drive out demons by Beelzebul, by whom do your followers [υἱός (huios)] drive them out? So then, they will be your judges." (Luke 11:19)
“The people [υἱός (huios)] of this age marry and are given in marriage. But those who are considered worthy of taking part in the age to come and in the resurrection from the dead will neither marry nor be given in marriage, and they can no longer die; for they are like the angels. They are God's children, since they are children [υἱός (huios)] of the resurrection." (Luke 20:34-36)
We can see from the above that the Greek word υἱός (huios) is being translated to subjects of the kingdom; people of the kingdom; daughter of Zion; child of hell; guests (actually better translated to servants) of the bridegroom; children of the Most High; followers; and children of this age

With each of these uses of the word, there is the subject - υἱός (huios) - and there is the person or thing that subject is subjected to. In the above uses, they are, respectively, kingdom, kingdom, Zion, hell, bridegroom, Most High and this age.

Now we come to the use with respect to God - as the word is used in the phrase, υἱὸς τοῦ θεοῦ - whereby τοῦ means "of" and θεοῦ refers to the Supreme Being.

As we see with the above uses of υἱὸς - being a subject of someone or something else - again combined with the Lexicon's meaning:
"used to describe one who depends on another or is his follower."
Again, we find the appropriate translations to this word υἱός (huios) with respect to ones relationship with the Supreme Being relates to being a follower, devoted servant or God's representative - depending of course on the context.

This parallels with the use of the word בֵּן (ben) in the Old Testament. While this word is sometimes translated to "son," it also has this same meaning when utilized in a devotional context. This is confirmed in Thayer's lexicon, as it is stated:
"[בֵּן (ben)] is a subject, rendering obedience to a king, or lord" and "a disciple, inasmuch as teachers were treated with reverence and obedience, like parents, and received the title of father. Hence, 'sons of the prophets,' for disciples of the prophets and the schools of the prophets themselves... 'sons of the magi,' used for the disciples of the magi among the Greeks (υἱοῖς) i.e., 'disciples' ..."
For further evidence for the appropriate translation of υἱὸς τοῦ θεοῦ, see this page.