"We believe that Jesus died and rose again and so we believe that God will bring with Jesus those who have fallen asleep in him." NIV translation
Why do we not have to grieve? The answer is simply that, as Christians, we are raised with Christ just as He was. Death has no power of us because sin and death were nailed to the cross. We simply fall asleep and wake up with Jesus in the twinkling of an eye.
"According to the Lord's own word, we tell you that we who are still alive, who are left till the coming of the Lord, will certainly not precede those who have fallen asleep." NIV translation
Paul describes the rapture of the church and reminds the readers of the fact that this is what Jesus said concerning the subject. The dead will be raised with Christ and those that are still here will then be caught up to join them in the air.
"For the Lord himself will come down from heaven, with a loud command, with the voice of the archangel and with the trumpet call of God, and the dead in Christ will rise first." NIV translation
Jesus is coming back when the Father gives the command. God has used a trumpet to call His people and to get them to move since the time of Moses and the wandering in the wilderness. He is going to do the same thing in the future as we see in Revelation 8.
"After that, we who are still alive and are left will be caught up together with them in the clouds to meet the Lord in the air. And so we will be with the Lord forever." NIV translation
Paul now describes what we commonly call "the rapture of the church" We will be going up to join the dead which have risen first and Jesus. We have the hope and the promise that we will be with the Lord forever.
"Therefore encourage each other with these words." NIV translation
Because of this confidence that we have and our knowledge about the coming Day of the Lord, we can be encouraged. Paul tells us to also strengthen others in the faith with this knowledge.