No one has ever seen God the Father. That's what the verse is referencing.
How about we look at the NIV:
"No one has ever seen God, but the one and only Son, who is himself God and is in closest relationship with the Father, has made him known."
Or the ESV:
"No one has ever seen God; the only God, who is at the Father’s side, he has made him known."
Or the KJV:
"No man hath seen God at any time; the only begotten Son, which is in the bosom of the Father, he hath declared him."
Now let's break these verses apart and add in the personages of the Trinity.
NIV:
No one has ever seen [the Father], but the one and only Son, who is himself God and is in closest relationship with the Father, [who] has made him known.
ESV:
"No one has ever seen [the Father]; the only [Son], who is at the Father’s side, he has made him known."
KJV:
"No man hath seen [the Father] at any time; the only begotten Son, which is in the bosom of the Father, he hath declared him."
Now let's look at the Greek:
Θεὸν οὐδεὶς ἑώρακεν πώποτε; μονογενὴς Θεὸς, ὁ ὢν εἰς τὸν κόλπον τοῦ Πατρὸς, ἐκεῖνος ἐξηγήσατο.
A direct translation would be:
God [The Father], no one has seen ever/as of yet; [the] only begotten God [the Son], the [one] being in the bosom/at the side of the Father, he has made [him] known.
Or more simply:
No one has ever seen the Father as of yet; the only begotten Son, being in the bosom/at the side of the Father, has made Him known.
Now, let's look at how the JW's phrase it:
No man has seen God at any time; the only-begotten god who is at the Father’s side is the one who has explained Him.
The JW's believe that Jesus is not God, as shown in John 1:1, and so dilute the real Gospel.
The Jehovah's Witnesses claim the end of John 1:1 reads as "and the Word [Christ] was a god," when in fact, the Greek phrases it perfectly clearly:
καὶ Θεὸς ἦν ὁ Λόγος
And God was the Word
Not, and a god was the Word, but simply, and God was the Word.
The Trinity is the only true God. Three in One, and One in Three.
Or, in the words of the Athanasian Creed:
"Whosoever will be saved, before all things it is necessary that he hold the catholic faith. Which faith except every one do keep whole and undefiled, without doubt he shall perish everlastingly.
And the catholic faith is this, that we worship one God in Trinity, and Trinity in Unity; Neither confounding the Persons, nor dividing the Substance. For there is one Person of the Father, another of the Son, and another of the Holy Ghost. But the Godhead of the Father, of the Son, and of the Holy Ghost is all one: the glory equal, the majesty coeternal. Such as the Father is, such is the Son, and such is the Holy Ghost. The Father uncreated, the Son uncreated, and the Holy Ghost uncreated. The Father incomprehensible, the Son incomprehensible, and the Holy Ghost incomprehensible. The Father eternal, the Son eternal, and the Holy Ghost eternal. And yet they are not three Eternals, but one Eternal. As there are not three Uncreated nor three Incomprehensibles, but one Uncreated and one Incomprehensible. So likewise the Father is almighty, the Son almighty, and the Holy Ghost almighty. And yet they are not three Almighties, but one Almighty. So the Father is God, the Son is God, and the Holy Ghost is God. And yet they are not three Gods, but one God. So likewise the Father is Lord, the Son Lord, and the Holy Ghost Lord. And yet not three Lords, but one Lord. For like as we are compelled by the Christian verity to acknowledge every Person by Himself to be God and Lord, So are we forbidden by the catholic religion to say, There be three Gods, or three Lords.
The Father is made of none: neither created nor begotten. The Son is of the Father alone; not made, nor created, but begotten. The Holy Ghost is of the Father and of the Son: neither made, nor created, nor begotten, but proceeding. So there is one Father, not three Fathers; one Son, not three Sons; one Holy Ghost, not three Holy Ghosts. And in this Trinity none is before or after other; none is greater or less than another; But the whole three Persons are coeternal together, and coequal: so that in all things, as is aforesaid, the Unity in Trinity and the Trinity in Unity is to be worshiped. He, therefore, that will be saved must thus think of the Trinity.
Furthermore, it is necessary to everlasting salvation that he also believe faithfully the incarnation of our Lord Jesus Christ. For the right faith is, that we believe and confess that our Lord Jesus Christ, the Son of God, is God and Man; God of the Substance of the Father, begotten before the worlds; and Man of the substance of His mother, born in the world; Perfect God and perfect Man, of a reasonable soul and human flesh subsisting. Equal to the Father as touching His Godhead, and inferior to the Father as touching His manhood; Who, although He be God and Man, yet He is not two, but one Christ: One, not by conversion of the Godhead into flesh, but by taking the manhood into God; One altogether; not by confusion of Substance, but by unity of Person. For as the reasonable soul and flesh is one man, so God and Man is one Christ; Who suffered for our salvation; descended into hell, rose again the third day from the dead; He ascended into heaven; He sitteth on the right hand of the Father, God Almighty; from whence He shall come to judge the quick and the dead. At whose coming all men shall rise again with their bodies, and shall give an account of their own works. And they that have done good shall go into life everlasting; and they that have done evil, into everlasting fire.
This is the catholic faith; which except a man believe faithfully and firmly, he cannot be saved."
