"For since death came through a man, the resurrection of the dead comes also through a man. For as in Adam all die, so in Christ all will be made alive." NIV translation
Paul reminds the believers of the fact that death is a result of the sin of Adam & Eve. All humans have the sin nature because we are all relatives of Adam & Eve. The final effect of sin is death and so all of our flesh will die at some point. Likewise, all will be made alive because of the fact that Jesus Christ defeated death when He was resurrected by the power of God. It is important to note that ALL people will be resurrected from the dead and not just those who have accepted Jesus Christ. There are many people that want to believe that the life we live now is all that there is but that is a lie from the devil.
"But each in turn: Christ, the firstfruits; then, when he comes, those who belong to him." NIV translation
As they say, "timing is everything" and Paul makes it clear that we will have our new bodies at the proper time. That proper time is when the Father sends Jesus back to get us and take us to be with Him. The final resurrection is for those that have died in their sin by rejecting the grace of God through Jesus Christ.
"Then the end will come, when he hands over the kingdom to God the Father after he has destroyed all dominion, authority and power. For he must reign until he has put all his enemies under his feet. The last enemy to be destroyed is death." NIV translation
Paul continues to speak about timing as he describes the time for Jesus' return. The phrase "has put everything under his feet" is a partial quote from Psalm 8. There, King David was worshiping God as he remembered the fact that the Creator of all things put man in charge of His creation. Man's pride has made many think that we are always going to be in control but judgment is coming when it will be made known that Jesus is Lord over all creation. Once that is established, Jesus will hand control back to the Father.
"For he 'has put everything under his feet.' Now when it says that 'everything' has been put under him, it is clear that this does not include God himself, who put everything under Christ. When he has done this, then the Son himself will be made subject to him who put everything under him, so that God may be all in all." NIV translation
Paul reminds us that God (the Father) is the ultimate authority and Jesus does His will. After Jesus (the King of Kings) has established the kingdom, it will be presented to the Father.