John 1:12-13

Yet to all who received Him, He gave the power to become sons of God, to those who believed in His name, who were born not of blood, nor of the will of the flesh, nor of the will of man, but of God.
John 1:12-13, Modern English Version (MEV)
 
We are guilty, in many ways, of cheapening the meaning of salvation, what it's all about. We have turned it into nothing more than a "get out of Hell free card" with a ticket to Heaven attached. We may talk about new birth, or re-birth, or of being born again, but it's mostly just lip service simply because few really understand what it means. This is most obvious when we hear believers describe themselves as "just a sinner saved by grace" or other similar associations. We still identify ourselves primarily with what we were rather than with what we are now. This partially explains why the Church is filled with so many weak and scripturally ignorant Christians.  Salvation is more than simply having our sins forgiven, although that is a big part of it. Salvation is more than simply getting a free pass out of Hell and into Heaven, although that certainly is a result of it. Salvation is about new birth and new life. It is a God thing because we certainly cannot bring about this rebirth. There is, in fact, nothing in this world that can, in anyway, cause anyone or anything to be born again. Only God can do this. And as if being born again isn't enough, in our new lives we have become children of God. If God says we are His children then how is it possible for us to say we are nothing more than a sinner saved by grace. Not me! I WAS a sinner, but God saved me by His grace and now I AM His child. 
 
We find the following in Matthew Henry’s Commentary of the Whole Bible:

That yet there was a remnant who owned him, and were faithful to him. Though his own received him not, yet there were those that received him (Jhn_1:12): But as many as received him. Though Israel were not gathered, yet Christ was glorious. Though the body of that nation persisted and perished in unbelief, yet there were many of them that were wrought upon to submit to Christ, and many more that were not of that fold. Observe here,
[1.] The true Christian's description and property; and that is, that he receives Christ, and believes on his name; the latter explains the former. Note, First, To be a Christian indeed is to believe on Christ's name; it is to assent to the gospel discovery, and consent to the gospel proposal, concerning him. His name is the Word of God; the King of kings, the Lord our righteousness; Jesus a Saviour. Now to believe on his name is to acknowledge that he is what these great names bespeak him to be, and to acquiesce in it, that he may be so to us. Secondly, Believing in Christ's name is receiving him as a gift from God. We must receive his doctrine as true and good; receive his law as just and holy; receive his offers as kind and advantageous; and we must receive the image of his grace, and impressions of his love, as the governing principle of our affections and actions.

[2.] The true Christian's dignity and privilege are twofold: -

First, The privilege of adoption, which takes them into the number of God's children: To them gave he power to become the sons of God. Hitherto, the adoption pertained to the Jews only (Israel is my son, my first-born); but now, by faith in Christ, Gentiles are the children of God, Gal_3:26. They have power, exousian - authority; for no man taketh this power to himself, but he who is authorized by the gospel charter. To them gave he a right; to them gave he this pre-eminence. This power have all the saints. Note, 1. It is the unspeakable privilege of all good Christians, that they are become the children of God. They were by nature children of wrath, children of this world. If they be the children of God, they become so, are made so Fiunt, non nascuntur Christiani - Persons are not born Christians, but made such. - Tertullian. Behold what manner of love is this, 1Jn_3:1. God calls them his children, they call him Father, and are entitled to all the privileges of children, those of their way and those of their home. 2. The privilege of adoption is entirely owing to Jesus Christ; he gave this power to them that believe on his name. God is his Father, and so ours; and it is by virtue of our espousals to him, and union with him, that we stand related to God as a Father. It was in Christ that we were predestinated to the adoption; from him we receive both the character and the Spirit of adoption, and he is the first-born among many brethren. The Son of God became a Son of man, that the sons and daughters of men might become the sons and daughters of God Almighty.

Secondly, The privilege of regeneration (Jhn_1:13): Which were born. Note, All the children of God are born again; all that are adopted are regenerated. This real change evermore attends that relative one. Wherever God confers the dignity of children, he creates the nature and disposition of children. Men cannot do so when they adopt. Now here we have an account of the original of this new birth. 1. Negatively. (1.) It is not propagated by natural generation from our parents. It is not of blood, nor of the will of the flesh, nor of corruptible seed, 1Pe_1:23. Man is called flesh and blood, because thence he has his original: but we do not become the children of God as we become the children of our natural parents. Note, Grace does not run in the blood, as corruption does. Man polluted begat a son in his own likeness (Gen_5:3); but man sanctified and renewed does not beget a son in that likeness. The Jews gloried much in their parentage, and the noble blood that ran in their veins: We are Abraham's seed; and therefore to them pertained the adoption because they were born of that blood; but this New Testament adoption is not founded in any such natural relation. (2.) It is not produced by the natural power of our own will. As it is not of blood, nor of the will of the flesh, so neither is it of the will of man, which labours under a moral impotency of determining itself to that which is good; so that the principles of the divine life are not of our own planting, it is the grace of God that makes us willing to be his. Nor can human laws or writings prevail to sanctify and regenerate a soul; if they could, the new birth would be by the will of man. But, 2. Positively: it is of God. This new birth is owing to the word of God as the means (1Pe_1:23), and to the Spirit of God as the great and sole author. True believers are born of God, 1Jn_3:9; 1Jn_5:1. And this is necessary to their adoption; for we cannot expect the love of God if we have not something of his likeness, nor claim the privileges of adoption if we be not under the power of regeneration.