After the Rapture will those left behind understand what happened and why?
The Bible doesn't say specifically what the world will think in response to the Rapture of the Church, but we know it will not produce widespread belief in the word of God. On the contrary, the supernatural judgments of God that take place during the end times only produce greater rebellion:
Rev. 9:20 The rest of mankind, who were not killed by these plagues, did not repent of the works of their hands, so as not to worship demons, and the idols of gold and of silver and of brass and of stone and of wood, which can neither see nor hear nor walk;
Rev. 9:21 and they did not repent of their murders nor of their sorceries nor of their immorality nor of their thefts.
If these judgments do not persuade hearts, then the disappearance of the Church will certainly not have much effect either. Furthermore, the apostasy of the last days foretold in the letter to Laodicea means that relatively few people will be taken away in the Rapture, and therefore the large number of people who will be left behind in the Church will likely convince many that the disappearances are not the Rapture but something else.
On the other hand, the Spirit of God will return to the earth following the Rapture, according to Revelation 7, and He will bring faith to a new generation of believers on earth in the final years prior to Jesus' return. Obviously, these new believers will have missed the Rapture, but the Bible testifies that their new faith in Jesus is not the product of the Rapture experience but of the work of the Holy Spirit in their heart, which is how all believers come to faith.
For a thorough understanding of the events of Tribulation, including the work of the 144,000 Jewish evangelists, please watch our Revelation Bible study series.
For more questions about this period, see our End Times topic section.