"Yes, Lord, walking in the way of your laws, we wait for you; your name and renown are the desire of our hearts. My soul yearns for you in the night; in the morning my spirit longs for you. When your judgments come upon the earth, the people of the earth learn righteousness." NIV translation
The phrase "way of your laws" speaks of "mishpat" or God's verdict (judgment) on sin. This passage speaks of the yearning of a Christian to be united with the Lord and how His disciples have waited intently for this Millennial Reign. We also see that this period of time is a time of learning as those who are left on the earth get to see the example of the righteous rule of Christ.
"But when grace is shown to the wicked, they do not learn righteousness; even in a land of uprightness they go on doing evil and do not regard the majesty of the Lord." NIV translation
As we see in Revelation 20, this thousand year period is a time without the influence of Satan. In the last days, people went so far as to blame everything on the devil and to say that, without his influence, they would be righteous.
This song now speaks of the fact that, even though Satan has been bound and has no more influence in the world, the people do not see that the problem is in their own hearts.
"Lord, your hand is lifted high, but they do not see it. Let them see your zeal for your people and be put to shame; let the fire reserved for your enemies consume them." NIV translation
It is sad as the song continues and acknowledges the fact that, even though God's grace has been put on display, men will still reject Jesus Christ. The Hebrew word that is translated as "zeal" is "qin'ah" and it speaks of jealousy like a husband who sees another man after his wife. As we have seen, this period of time is a time for those who have not accepted Jesus to see His love for His people and to be provoked to jealousy. Those who are not provoked to jealousy will face the rejection of Christ and the punishment of hell which was created for Satan and his followers.