What does "...his days will be a hundred and twenty years." in Genesis 6:3 mean?

Genesis 6:3
Then the Lord said, "My Spirit will not contend with man forever, for he is mortal (meaning corrupt); his days will be a hundred and twenty years."

AN INCORRECT ASSUMPTION BASED ON OBSERVATION
Most people read this Bible verse and make a quick incorrect assumption.  Looking around and observing their current culture they assume that what God is referring to is a limitation on man's potential lifespan.  We observe that nobody in modern culture is living longer than 120 years.  So we rush to an incorrect assumption without any evidence supporting this interpretation of scripture.  Let's look deeper for evidence to find the real meaning of this verse.

READING BASED ON CONTEXT
To interprete this verse correctly we must look at the rest of Genesis to determine both the nature of God and how He has dealt with man in the Old Testament and in the New Testament.  We must know that the Bible states God is never changing and shows both judgement & grace to mankind.  We must ask ourselves, in this verse is God punishing man without allowing repentance?  That is an important question to ask to understand God's nature.  Is it the nature of God to judge without first offering grace?  Let's look at evidence of God's nature.  In the first occurrence of sin in the Bible, God showed grace to Adam & Eve by clothing them after they sinned (Genesis 3:21) and punishment (Genesis 3:23-24).  God showed grace to Caine (Genesis 4:9) by asking "Where is your brother Abel?".  God hoped that Caine would realize the sinfulness of his action and repent.  Caine did not repent and God judged him (Genesis 4:11-12).  If we look for evidence of God's nature in the new testament, we see the exact same nature of God.  God is both gracious and a good judge.  From this and all other consistent traits, we can determine that the God of the Old Testament and the God of the New Testament are the same God.  So, if they are the same God and God never changes (Hebrews 13:8), then God would behave in the same manner.  You may ask yourself, why are we not judged in the same way today as in the Old Testament?  It's a good question.  We are under a new covenant, in fact New Testament means new covenant.  God is still merciful showing grace but also still judging mankind for sin.  Grace is provided through the sacrifice of Jesus Christ as atonement for sin.  We must repent of our sins and accept this atonement or like Caine, we will be subject to the full penalty of judgement.  By accepting the sacrifice that paid the penalty for our sins, we are forgiven.  The full penalty of judgement without humbling ourselves to accept the atonement is eternal separation from God in hell.

LIFESPANS IN THE YEARS IMMEDIATELY AFTER THE FLOOD
Were lifespans shortened after the flood?  Let's look to the genealogies that the Bible provides.  After the flood the descendants of Noah's sons Shem from Arphaxad to Abraham were:  Shem (600 years old), Arphaxad (438 years old), Salah (433 years old), Eber (464 years old), Peleg (239 years old), Reu (239 years old), Serug (230 years old), Nahor (148 years old), Terah (205 years old) and Abraham (175 years old).  We can see from this vertical genealogy that in the years after the flood not a single descendant of Shem all the way through Abraham lived less than 175 years.  So, we must assume that our original assumption that man would only be permitted to live 120 years due to his corrupt nature was an incorrect assumption.  So, we must re-read this verse and add up the evidence as to how God relates to man.

VERSE INTERPRETATION BASED ON CONTEXT
God is the same always, reacting with both grace and judgement.  We also know that man after the flood did not experience shorter lifespans.  Knowing this we need to read the verse again.  What is the 120 years God is referring to?  I strongly believe that the 120 years God is referring to is a direct offer of grace.  He is offering 120 years for mankind to repent or face annihilation by flood.  All those who repent will be saved and those who continue to seek a sinful  rejection of God will be dealt with severely.  From this command we can assume that Noah and his family worked not only on the ark but also in an attempt to turn the hearts of their fellow man toward God to no avail.  We see that mankind as a whole chose sin over God.  So God was merciful offering redemption yet none chose to be saved other than Noah and his family.

WHAT CAN A MODERN CHRISTIAN GAIN FROM THIS VERSE?
This story should encourage all of us who know Jesus.  The New Testament fulfills the Old Testament prophesy about the Messiah.  Jesus Christ is the Messiah who was promised.  He fulfilled scriptures becoming the ultimate sacrifice for sin.  He was the unblemished Lamb who was worthy to atone for all mankind's sin.  We see God's mercy and grace in the face of man's rebellion from the very beginning and we see God's call for repentance and his issuance of judgement.  We realize that God is love.  As it states in John 3:16, God loved us so much that he extended grace giving Jesus Christ as atonement for our sin knowing in advance that mankind as a whole would continue to rebel against Him.  He extended the grace to all yet many will reject him and instead choose the judgement.  Others will accept grace and the penalty that was due them will instead be placed on Christ.  Those who accept Christ have passed from death to life.  They will pass from this life directly into the loving embrace of God free of judgement.   So we see God is both gracious and a fair judge.  He does not lessen the penalty.  Instead, he differs the penalty from us directly to Christ for payment.  God is the same yesterday, today and forever.  He loves all of mankind and offers redemption.