Isaiah is one of the longest active prophets. He acted as prophet/historian for Judah for over 60 years. During this time he saw Israel captured by the Assyrians and prophesied that the same would happen to Judah. He was a prophet during the reign of 5 kings of Judah; Uzziah, Jotham, Ahaz, Hezekiah, and Manasseh. Most of these kings were good, except for the last in Manasseh who brought idol worship to Judah again.
Perhaps it was because of these good kings that Isaiah was able to give a ray of hope while delivering a message of doom. He told them how they were going to be captured and exiled from the promised land but extends the hope of salvation. Israel was not listening to the prophets and received no such message as Isaiah gave to Judah. In the book of Isaiah we see a lot of prophecies about Jesus.
There are two different prophecies in our passage. The first bit talks about Jesus. We see that the Spirit of God will lay on Jesus (Isaiah 11:2) which we see happen during his baptism (Luke 3:21-22). Jesus will not base judgment on appearance and seek justice for the poor (Isaiah 11:3-4) which is evidenced throughout his ministry. Verses 6-8 gives many examples of a gentle creature living with a dangerous one. This shows that Jesus will come and live on earth, the domain of Satan. Even mentioning Jesus as a baby and a little child showing he would come as a baby and grow into an adult.
The second half of the passage is the prophecy of both Israel and Judah returning from exile. The scattered Jewish people from all over (Isaiah 11:11) will all come back under one flag and reunite together (Isaiah 11:13). God will guide them back to the promised land and they will be his people once again.
Isaiah prophesies Judah's exile about 130 years before it happens, prophesies Israel and Judah's return 177 years before that happens, and prophesies about Jesus 720 years before he is born. God's plans stretches throughout the ages and His word always comes true.