"Therefore my people will go into exile for lack of understanding; their men of rank will die of hunger and their masses will be parched with thirst. Therefore the grave enlarges its appetite and opens its mouth without limit; into it will descend their nobles and masses with all their brawlers and revelers. So man will be brought low and mankind humbled, the eyes of the arrogant humbled." NIV translation
The people have turned their backs on the Lord and decided to do what they wanted instead of following God's rules. The scene is much the same as most parents have with their teenage children at some point. The children decide they don't want to follow the rules in the home and want to go live someplace else. That is what "exile" is in this passage. God has basically said that, since the people will not follow his rules, they will be sent to live someplace else where they will learn what it is like to live under an earthly ruler instead of having God, who loves them, as ruler and king. Their arrogance in thinking they know better than God will lead them to the grave.
"But the Lord Almighty will be exalted by his justice, and the holy God will show himself holy by his righteousness." NIV translation
Even after disciplining his people, God will be lifted up as everyone will know that it is righteous justice. The people deserved what they got. God will show himself to be holy because he removes the sinful people from his presence. Just as it has always been, God does not tolerate sin in his presence. We, as Christians, do not have to face his righteous justice because Jesus did so in our place on the cross.
"Then sheep will graze as in their own pasture; lambs will feed among the ruins of the rich." NIV translation
After the sinful people have been exiled and God is exalted, there will be peace. Sheep and lambs are left in the land. We, as Christians, are described as sheep and lambs all throughout the New Testament and this verse is an illustration for us of God's righteous judgment. With Jesus as our shepherd, we get to remain in the land and have a right relationship with God.
"Woe to those who draw sin along with cords of deceit, and wickedness as with cart ropes, to those who say, 'Let God hurry, let him hasten his work so we may see it. Let it approach let the plan of the Holy One of Israel come, so we may know it.'" NIV translation
The picture here is of someone drawing out strands of fibers to make a rope. The woe comes to those who mix good cords with bad to make an inferior rope. The rope looks good on the outside but it is not strong like it should be with multiple good cords. When the rope is used under stress, it will break. It is also a picture of the "Christian" who says and does the proper things when at a "church" but there has been no change in their heart and acceptance of Jesus Christ. When they meet the Judge on that day, Jesus will say that he never knew them and they will be cast away.