Let's examine what the Scripture has to say about God's children...
11 He came to his own, and his own people did not receive him. 12 But to all who did receive him, who believed in his name, he gave the right to become children of God, 13 who were born, not of blood nor of the will of the flesh nor of the will of man, but of God. John 1:11-13 (ESV)
15 For you did not receive the spirit of slavery to fall back into fear, but you have received the Spirit of adoption as sons, by whom we cry, “Abba! Father!” 16 The Spirit himself bears witness with our spirit that we are children of God, 17 and if children, then heirs—heirs of God and fellow heirs with Christ, provided we suffer with him in order that we may also be glorified with him. Romans 8:15-17 (ESV)
1 See what kind of love the Father has given to us, that we should be called children of God; and so we are. The reason why the world does not know us is that it did not know him. 2 Beloved, we are God's children now, and what we will be has not yet appeared; but we know that when he appears we shall be like him, because we shall see him as he is. 3 And everyone who thus hopes in him purifies himself as he is pure. 1 John 3:1-3 (ESV)
The children are the children of God or more specifically those who belong to God the Father. They are His sons and daughters, through their sincere faith-belief-trust-confidence in His Son Jesus Christ as their personal Lord and Savior.
Let's now move on to discover what the scripture says about: