The infrequently used word "furtherance" (meaning simply "advancement") occurs elsewhere only in Philippians 1:25, where Paul speaks of the "furtherance and joy of faith," which he hoped to see in the Christians at Philippi, and in 1 Timothy 4:15, where it is translated "profiting." There, Paul urged young Timothy to continue studying the things of God "that thy profiting may appear to all."
Paul wrote this epistle while he was unjustly imprisoned in a Roman jail, and no doubt he remembered the time when he had first met many of his Philippian Christian friends as a result of being imprisoned and beaten in a Philippian jail (Acts 16:12-40). In fact he had often been imprisoned (2 Corinthians 11:23) and had suffered severely in many other ways for "the furtherance of the gospel."
Indeed, during the two years or more he was a prisoner in Rome, he not only taught God's Word to many who visited him there (Acts 28:30-31) but also wrote at least four of his inspired epistles there (Ephesians, Philippians, Colossians, Philemon--possibly even Hebrews). And these have been of untold blessing to millions down through the years. In ways which Paul could never have imagined, it was true indeed that these things which had happened to him had "fallen out rather unto the furtherance of the gospel."
The apostle Paul had the spiritual insight to realize that what seemed like great problems and difficulties could be used by God to the "advancement" of the gospel. Rather than complaining or even quitting when the Christian life gets hard, we must remember that God can make even "the wrath of man" to bring praise to Him (Psalm 76:10). HMM