The context of this verse says, "For then shall be great tribulation, such as was not since the beginning of the world to this time, no, nor ever shall be. And except those days should be shortened, there should no flesh be saved: but for the elect's sake those days shall be shortened." (Matthew 24:21,22)
This tribulation is also mentioned in Daniel 12:1, "…there shall be a time of trouble, such as never was since there was a nation even to that same time: and at that time thy people shall be delivered…"
These and other scriptures show that there is trouble coming on this earth that could end up destroying everyone on the earth. During these last days, we will see, "Men's hearts failing them for fear, and for looking after those things which are coming on the earth…” Luke 21:26
However, God does not want us to be afraid of this. Along with these tribulation prophecies, He also gives us hope. He shows that He is still in control of everything, and He will shorten those days…not that the individual days will be less than 24 hours, but that the trouble of these days will not be allowed to get to the point of destroying everyone. He will only allow this to go on until the lesson is learned. Mankind needs to recognize that without Him all flesh would be destroyed.
God has always preserved a “remnant” in times of tribulation. When the flood came, He saved Noah and his family. When the nation of Israel was overthrown, He again preserved a faithful remnant. God saved some Jews in order to regather and reestablish the nation of Israel as was prophecized in Ezekiel 37. Today, we rejoice to see the beginning of the fulfillment of this promise.
In Matthew 24:21,22, it says for the elect's sake those days shall be shortened. The Holman Bible says "But those days will be limited because of the elect." Other translations say, "on account of the elect". It is the elect (those faithful Christians who will be raised to a heavenly life) who will be working with our Lord Jesus to shorten these days and bring the blessings of the Gospel. Galatians 3:8: "And the Scripture, foreseeing that God would justify the Gentiles by faith, preached the gospel beforehand to Abraham, saying, 'ALL THE NATIONS SHALL BE BLESSED IN YOU.'"
During Christ’s reign, the nations “shall not hurt nor destroy…for the earth shall be full of the knowledge of the LORD as the waters cover the sea.” Isaiah 11:9. People will not want to repeat the mistakes of the past, which would have brought their destruction, but will learn to follow God's law of love, and be able to truly say with the angels, "Glory to God in the highest, and on earth peace, good will toward men."