At the rapture, will those that are left behind realize what just 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:
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.
For more questions about this period, see our End Times topic section.