Jamieson, Fausset and Brown on Colossians 1:10

10. Greek, "So as to walk"; so that ye may walk. True knowledge of God's will is inseparable from walking conformably to it.

worthy of the Lord--(Ep 4:1).

unto--so as in every way to be well-pleasing to God.

pleasing--literally, "desire of pleasing."

being fruitful--Greek, "bearing fruit." This is the first manifestation of their "walking worthy of the Lord." The second is, "increasing (growing) in the knowledge of God (or as the oldest manuscripts read, 'growing BY the full knowledge of God')"; thus, as the Gospel word (Col 1:6) was said to "bring forth fruit," and to "grow" in all the world, even as it did in the Colossians, ever since the day they knew the grace of God, so here it is Paul's prayer that they might continue to "bring forth fruit," and "grow" more and more by the full knowledge of God, the more that "knowledge" (Col 1:9) was imparted to them. The full knowledge of God is the real instrument of enlargement in soul and life of the believer [Alford]. The third manifestation of their walk is (Col 1:11), "Being strengthened with all might," &c. The fourth is (Col 1:12), "Giving thanks unto the Father," &c.