How often have you heard someone say "Were all God's children"? It is not unusual for the term Father to be used when speaking of God, at least in Christian circles. Jesus did so, and instructed his followers to do the same when teaching them to pray. However, this not only speaks of God's paternal characteristics towards us, but it also speaks of our relationship to Him. It is this relationship, of us to God as children, that I want to consider.
First, it cannot be said that just anyone is a child of God. Though He did create us all, there has been a fall and separation that must be atoned for and taken out of the way. As Paul said, "For you are all sons of God through faith in Christ Jesus. For all of you who were baptized into Christ have clothed yourselves with Christ". So it is clear that the qualification for status as a child is faith and baptism in Christ. Again, as John wrote, "To all who received Him, to those who believed in His name, He gave the right to become children of God".
Don't let the blessing and privilege of this be lost on you. This is not something that we are born into like our natural sonship, it is adoptive. Thus we are chosen and it is solely by a gift of grace. We are heirs along with Christ. We are brothers and sisters of Jesus.
What does it mean to me that God is my Father? This is a quite comfortable and comforting question. All the answers that you may come up with probably make you feel cozy and require nothing from you. However, there is a question that follows that is less comfy: What does it mean to me that I am God's child? If I may put it another way: we are quick to elaborate on what the Father-son relationship means to us in terms of benefits, but slow to consider what it means in terms of responsibilities and expectations.
You see, Christianity isn't just a "one and done" deal. It's not just fire insurance. Being a child of God signifies that He is in a position of authority over us. It suggests a sense of affection and fellowship between us. And it means giving honor to Him in all these areas. When Jesus called his followers to live in a certain way it was always to either imitate, glorify, or please the Father.
While works do not save us, they are and must be a developing "family trait". As children of God, we do no follow the law to sustain our salvation, but as J.I. Packer wrote, "Law-keeping is the family likeness of God's children; Jesus fulfilled all righteousness, and God calls us to do likewise."
You cannot give the Bible even a cursory reading without finding a strong theme of God's Fatherhood over us. Yet there are so many who passively call God "Father" and live like anything but His child. Anyone who isn't being made into an obedient child of God, no matter how faltering or stumbling, may be no child at all. If there is no love, no deference to the will of the Father, no grief at sinning against such a loving parent, one should rightly ask themselves if He is truly Father. If the Bible gives clear guidelines as to what a true child adopted into all rights and benefits looks like, we would be wise to ensure our lives mirror that.
For a more in-depth treatment of the subject, see Knowing God by J.I. Packer, specifically the chapter "Sons of God".