This thousand-year reign of Christ, also called the Millennium, offers people who have not known Christ or His true expectations an opportunity to respond to Him. It is important to note that this is not a second chance. It will be the first and only chance for these people. The Bible teaches that everyone will have an opportunity to come to God (2 Peter 3:9).
For those called today, the firstfruits, the opportunity (judgment) is now (1 Peter 4:17). Others will have this opportunity during the Millennium.
As for those who are alive at the start of the Millennium, these people are ones who will have lived through the cataclysmic events of the return of Jesus Christ—called the "day of the Lord" in the Bible. Their physical lives will continue as the Kingdom of God is established here on earth (Revelation 5:10).
As to what the life span of human beings during the Millennium will be, the Bible doesn't explicitly say. It probably will be at least as long as people live today, and perhaps longer (see Zechariah 8:4). People will have children (verse 5). One important change in human life during this time, however, will be the interaction of the spirit world with human beings.
During the Millennium, Satan will be bound (Revelation 20:1-2) and the firstfruits, God's people who will have been changed into spirit at Christ's return (1 Corinthians 15:52), will be actively teaching people God's ways.
Commenting on this time, Isaiah 30:20-21 says: "And though the Lord gives you the bread of adversity and the water of affliction, yet your teachers will not be moved into a corner anymore, but your eyes shall see your teachers. Your ears shall hear a word behind you, saying, 'This is the way, walk in it,' whenever you turn to the right hand or whenever you turn to the left."
Satan's constant influence to cause people to sin, which is part of this present evil world, will be replaced by spirit beings who will help guide people into godly paths.
Because of this positive teaching and guidance by spirit beings and the fact that God's law will be going out to all the earth from Jerusalem (Isaiah 2:2-3), it seems that people living in the Millennium will know about this period of time and that this is their opportunity to respond to God.