What does it mean, to walk worthy of the Lord?

Colossians 1:10 That ye might walk worthy of the Lord unto all pleasing, being fruitful in every good work, and increasing in the knowledge of God;

To walk worthy of the Lord, is to obey the Lord or to conduct oneself (i.e. walk) in a manner which the Lord finds pleasing or meritorious (i.e. worthy).

The statement, to walk worthy of the Lord, has the Judgment strictly in view. The Apostle is admonishing us to do the righteous things which God requires of us if we want to receive eternal life. As it is written:

Romans 2:6 Who will render to every man according to his deeds:
7 To them who by patient continuance in well doing seek for glory and honour and immortality, eternal life:
8 But unto them that are contentious, and do not obey the truth, but obey unrighteousness, indignation and wrath,
9 Tribulation and anguish, upon every soul of man that doeth evil, of the Jew first, and also of the Gentile;
10 But glory, honour, and peace, to every man that worketh good, to the Jew first, and also to the Gentile:
11 For there is no respect of persons with God.
12 For as many as have sinned without law shall also perish without law: and as many as have sinned in the law shall be judged by the law;
13 (For not the hearers of the law are just before God, but the doers of the law shall be justified.