I. The Righteous Reign of The Branch (1-5)
Out of the stump that were left from the judgment, a branch will grow out of Jesse's line. Jesus was a descendant of Jesse through Mary (v1). Why didn't Isaiah say "branch of David", since David was a lot more famous to the hearers? I believe God deliberately said it this way to emphasize the humble beginning of the Messiah, and not to play up the political card.
True to the prophecy, the Spirit of the Lord literally came and rested on Jesus during His baptism: "And when Jesus was baptized, immediately he went up from the water, and behold, the heavens were opened to him,c and he saw the Spirit of God descending like a dove and coming to rest on him; and behold, a voice from heaven said, “This is my beloved Son,d with whom I am well pleased.” (Mat 3:16,17)
Some people ask why must the Spirit come to Jesus, if He was already the Messiah at birth. I believe Jesus already have the Spirit of God inside him, but this is a public demonstration to everyone there of His anointing and His position as the Son of God.
Verse 3 to 5 describe His roles. It seems that He has the supernatural ability to know the situation of each person - that He does not need to judge based on outer appearances but is able to judge with righteousness what is equitable to all.
He is not only the judge, but also the executioner - to be able to take away life with his words. This would be scary if such power is given to any human being, but Jesus will be a benevolent ruler, with perfect righteousness and faithfulness. (v5)
II. Transformation of Nature (6-10)
Another great miracle is the transformation of nature. When the Son of God rules, there will be no more predators - the lions, leopards, and bears will not kill the preys but will become herbivours. (v6-7). In addition, the relationship between man and the animals will be restored (the way it was before Noah), such that a child can play with the snakes. (v8).
"The fear of you and the dread of you shall be upon every beast of the earth and upon every bird of the heavens, upon everything that creeps on the ground and all the fish of the sea. Into your hand they are delivered. Every moving thing that lives shall be food for you. And as I gave you the green plants, I give you everything." (Genesis 9:2-3)
The whole earth will have knowledge of the Lord. It is not just knowing Him in faith or in doubt, but the way we know our prime minister today - everyone knows He exists and His works on earth. The nations will come and inquire from Him. (v9,10)
III. The remnant (11-16)
Today, the Jews in Israel are from the tribe of Judah and Benjamin. (That's why they are called "Jews", i.e. from the tribe of Judah.) The ten other tribes in Israel were exiled by the Assyrians in 722 BC, and had never returned. However, God promised that there will be a reunification one day:
"Say to them, Thus says the Lord GOD: Behold, I am about to take the stick of Joseph (that is in the hand of Ephraim) and the tribes of Israel associated with him. And I will join with it the stick of Judah, and make them one stick, that they may be one in my hand... then say to them, Thus says the Lord GOD: Behold, I will take the people of Israel from the nations among which they have gone, and will gather them from all around, and bring them to their own land. And I will make them one nation in the land, on the mountains of Israel. And one king shall be king over them all, and they shall be no longer two nations, and no longer divided into two kingdoms." (Ezekiel 37:19-22)
Here in Isaiah, it speaks about the places where the people will come from. The names of the countries may be obsolete, but the geographical places are still there. Apparently, the exiles have turned the Israelites into natives of different lands such as Assyria, Egypt, Pathros, Cush, and from "four corners of the earth" (v11,12). In verse 16, Isaiah described a "highway" from Assyria, which is literally there today from Turkey and Iraq.
We don't know how, but there will some way to identify them (medically?), when God "raise a signal", and those that have lost their ancestral linkages will know who they were.
Since there are wars being described here (v14-15), it may suggest that the reunification may happen before or during the tribulation period, and this was described in Revelation during the sixth-seal:
"And I heard the number of the sealed, 144,000, sealed from every tribe of the sons of Israel:" (Rev 7:4) and it went on to list all the tribes of Israel. The sealing of the tribes protects them from subsequents plagues during the tribulation.
And when they return, the conflict and jealousy between the brothers will be gone. They will reunite and combine their strengths against their enemies during the tribulation period.