The significance of this statement by the Apostle Paul is literally that the holy Scriptures are God-breathed. God not only gave a universe to witness of His greatness as the Creator, He also gave us a written transcript of His very words.
Many people object to this and try to attribute human shortcoming to the Book based on the men who wrote it down. However, it is plain that the Bible teaches within itself that though God used human penmen, He superintended and overruled so that what they wrote was and is the breath of His lips, His spoken word. To say God could not do such a thing is a profession of atheism. Nothing is too hard for the Lord.
In Psalm 19, where the Psalmist begins by saying that the heavens declare God's glory, the later verses are about the special witness of God given by His Word. The Bible gives us truths about God and our relationship to Him that can be known no other way. While we have a certain consciousness of right and wrong in ourselves, only by the Bible can we know of God's absolute and perfect standard of right and wrong, God's law.
Only by the Bible can we know the full consequences of sin on the human race. Only by the Bible's history can we know with certainty the origin of the world, of man, or of sin. Only by His prophecy can we know with equal certainty the future for the world and for ourselves individually. And only by the written word can we know of God's simple but profound plan of salvation to bring those who believe to heaven when they die.
One of the terms used for the Bible within the Bible is God's Testimonies. "Blessed are they that keep his testimonies, and that seek him with the whole heart" (Psalm 119:2). God Himself has condescended to take the witness stand and speak about the matters of man's spiritual life and needs, and has written it all down so we can know for sure what our eyes and wit could never perceive on their own. It remains for us to search them out with all our heart and to have a willingness to accept it as the testimony of the One who knows all things and who cannot lie.