"No, this is what was spoken of by the prophet Joel: "In the last days, God says, I will pour out my Spirit on all people. Your sons and daughters will prophesy, your young men will see visions, your old men will dream dreams."" NIV translation
Peter is now using the Old Testament (Torah) to explain what is going on. Most of the crowd was probably Jews and the Torah was all that they new about God. He is basically telling them that what is written in the Torah is happening before their eyes. We can also learn a little from this quote from Joel. It says "In the last days" God would pour out his Spirit. We, as Christians, have had that Spirit poured out on and into us and, as the quote goes on to say, it is for everyone. That should make us sit up and take notice that we are indeed in the last days. That should also give us a focus of purpose in telling others about our Savior.
"Even on my servants, both men and women, I will pour out my Spirit in those days, and they will prophesy. I will show wonders in the heaven above and signs on the earth below, blood and fire and billows of smoke." NIV translation
Peter is still quoting the prophet Joel to the crowd. He is still talking about the last days. He again says that the gift of the Spirit is for everyone. Then, he goes on to predict wonders in the heaven and signs on the earth. These wonders happened on the day that Jesus was crucified. We are told in the gospel accounts that, on that day, it was dark in the middle of the day.
We are also told of the curtain in the temple being torn in two. These events would still be in the memory of many of the people in this crowd.
"The sun will be turned to darkness and the moon to blood before the coming of the great and glorious day of the Lord. And everyone who calls on the name of the Lord will be saved." NIV translation
Peter is still quoting from the prophet Joel here. The first part, with the darkness and blood red moon actually happened when Jesus was crucified. The last part is such an awesome promise but also is a stumbling block for many. It seems like it is too easy to be saved by just calling on the name of the Lord but that is what it says. Many want to add a bunch of rules or other things but it really is that simple to be saved.
""Men of Israel, listen to this: Jesus of Nazareth was a man accredited by God to you by miracles, wonders, and signs, which God did among you through him, as you yourselves know."" NIV translation
Now, Peter is still addressing the crowd of Jews but he shifts from quoting the prophet Joel to reasoning with them about Jesus. He points out that they even saw the signs, miracles, and wonders that God did through Jesus. In life, it is much easier to dismiss talk than it is actions. Peter is reminding them that they not only heard the talk but they seen the walk from Jesus. How are you doing in demonstrating your walk and not just talking the talk? Walking the way of Jesus, my friends, that is the way to reach people. As they say, talk is cheap.