Some Christians do not believe that there will be a rapture of true believers in Christ. I don't know how they get around the common understanding of the verses below. I agree with them that the word rapture is not found in the Bible, it is a word used to describe the Church, the people of God, being caught up to meet the Lord at His coming. The English word comes from the Latin word rapere, meaning rapid. The Latin phrase rapere is from the original Greek word, harpazō, translated as “caught up” in the King James Bible and English Standard Version, as in the passage below. Harpazō means: "to strip, spoil, snatch. To seize upon with force; to rob. It is an open act of confiscatory violence. To snatch or tear away, yank away, pluck out of, remove by swiftly and aggressively grasping." Here’s the passage in the Scriptures that talk about the people of God being “caught up.”
13But we do not want you to be uninformed, brothers, about those who are asleep, that you may not grieve as others do who have no hope. 14For since we believe that Jesus died and rose again, even so, through Jesus, God will bring with him those who have fallen asleep. 15For this we declare to you by a word from the Lord, that we who are alive, who are left until the coming of the Lord, will not precede those who have fallen asleep. 16For the Lord himself will descend from heaven with a cry of command, with the voice of an archangel, and with the sound of the trumpet of God. And the dead in Christ will rise first. 17Then we who are alive, who are left, will be caught up together with them in the clouds to meet the Lord in the air, and so we will always be with the Lord. 18Therefore encourage one another with these words (1 Thessalonians 4:13-18 ESV).
There is coming a time when the Lord Himself will descend from heaven with a shout and at that instant, those in Christ will be snatched from this earth and changed as we are gathered together to be forever with Christ. It goes along with what Paul wrote to the Corinthians about the change in our nature, and also when the trumpet is sounded:
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.” 53For the perishable must clothe itself with the imperishable, and the mortal with immortality (1 Corinthians 15:52-53).
This word, changed, what does it mean? That which is on the inside, the real you, the character that God has been working on throughout your life, will someday be revealed. It won't be the same as the old nature that we inherited from Adam; Paul says that flesh and blood cannot inherit the kingdom of God (1 Corinthians 15:50). Our new bodies will no longer be perishable but imperishable (15:53). We won’t all go through the sleep of death; there will be those on earth who will be transformed instantly. This transformation is the rapture or being caught up, whichever word you wish to use. When Christ comes, in a flash, in the batting of an eye’s time, we will be changed from having a perishable body to being clothed with an imperishable body as in the verses above. Paul also wrote to the Philippian church about this change:
...the Lord Jesus Christ, 21who, by the power that enables him to bring everything under his control, will transform our lowly bodies so that they will be like his glorious body (Philippians 3:20-21 Emphasis mine).
Isn’t this your longing and desire, to be like Jesus? This word translated transform is the Greek word Metaschēmatizō. It is a construction of two Greek words. Meta means a change of place or condition, and schēma meaning shape, or outward form. To transform, change the outward form or appearance of something, to refashion, reshape. There is a rapture of the saints at the coming of Jesus, a transformation. That which is on the inside will be revealed—and it will be glorious:
2Multitudes who sleep in the dust of the earth will awake: some to everlasting life, others to shame and everlasting contempt. 3Those who are wise will shine like the brightness of the heavens, and those who lead many to righteousness, like the stars for ever and ever (Daniel 12:2-3).
 Key Word Study Bible, AMG Publishers. 773 Harpazō.  Key Word Study Bible, AMG Publishers, Page 1651.