"Listen, I tell you a mystery: We will not all sleep, but we will all be changed - in a flash, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, the dead will be raised imperishable and we will be changed." NIV translation
The mystery that Paul speaks of is commonly called "the rapture" or the time when Jesus comes back to gather His people. As we see, we are not all going to die and be buried in the ground. If you are in Christ and He returns while you are still alive, you do not die but you are changed into your spiritual body to be like Him.
"For the perishable must clothe itself with the imperishable, and the mortal with immortality." NIV translation
These earthly bodies will not enter heaven and so everyone must be changed. It is like putting on new clothes for a special event but these new clothes will last forever.
"When the perishable has been clothed with the imperishable, and the mortal with immortality, then the saying that is written will come true: 'Death has been swallowed up in victory.' 'Where , O death, is your victory? Where, O death is your sting?'" NIV translation
With the return of Christ and these new bodies, there will be no more death. The victory has been won through the death, burial, and resurrection of Jesus Christ.
"The sting of death is sin, and the power of sin is the law." NIV translation
The cause of death for our earthly bodies is sin and sin gets its power to cause death through our inability to keep the law of God. Without the law, there would have been no basis for fair judgment of disobedience (sin).
"But thanks be to God! He gives us the victory through our Lord Jesus Christ." NIV translation
We did not have the ability to keep the law perfectly but Jesus did on our behalf. He not only did that but He also paid the penalty for our sins and so we have overcome death and moved to eternal life.
"Therefore, my dear brothers and sisters, stand firm. Let nothing move you. Always give yourselves fully to the work of the Lord, because you know that your labor in the Lord is not in vain." NIV translation
Paul concludes his teaching on the resurrection body by urging the believers to hold fast to what they know. He also urges them to put their faith into action by serving the Lord.