And he came to Nazareth, where he had been brought up. And as was his custom, he went to the synagogue on the Sabbath day, and he stood up to read. And the scroll of the prophet Isaiah was given to him. He unrolled the scroll and found the place where it was written,
“The Spirit of the Lord is upon me,
because he has anointed me
to proclaim good news to the poor.
He has sent me to proclaim liberty to the captives
and recovering of sight to the blind,
to set at liberty those who are oppressed,
to proclaim the year of the Lord's favor.”

And he rolled up the scroll and gave it back to the attendant and sat down. And the eyes of all in the synagogue were fixed on him. (Luke 4:16-20)

To the listeners, these would have been familiar verses from Isaiah - spoken about the Messiah, God’s anointed one, the one that God would send to rescue the people. At Isaiah’s time the people were in exile in Babylon and this represented the promise that they wouldn’t always be there - they would go back to their land, God hadn’t forgotten about them. One day God was going to send someone and sort it all out, putting everything back as it should be.

To the Jews at Jesus time it represented hope for people living under roman rule. It’s not always going to be like this, God has not forgotten us, one day he is going to send someone to sort this all out. The Romans will be gone, the temple will be purified, God’s enemies will be wiped out, the nation of Israel will be back to the glory days.

So after Jesus reads those verses, all eyes are on him - they all knew about the rumours that Jesus might be this messiah. What was he going to say now? Here’s how we take down the Romans? Here’s how we more closely follow the purification laws? Here’s how we redistribute the land and wealth more fairly? He doesn’t say any of that

And he began to say to them, “Today this Scripture has been fulfilled in your hearing.” (Luke 4:21)

Whatever they took away from it, and evidence later in the chapter shows that they didn't really get what Jesus was saying, they certainly knew that this was a big deal. Remember all these things that God promised hundreds of years ago? 
They are being fulfilled. 
In me.