(Note: Most of the answers given so far are based on the penal substitution model of atonement, which is confined largely to the Protestant wing of Christianity. However, this question was asked in the early days of Christianity.SE, before current standards were adopted regarding this site being about Christianity, not about the truth. (See "We can't handle the truth.") Most answers so far were therefore framed as "truth" answers--which would today be contrary to site guidelines--rather than providing their denominational or doctrinal framework to mark them as answers about Christianity.)
As a late answer to an old question, I will state at the outset that this answer is given from the perspective of the theology of Emanuel Swedenborg (1688-1772), and of the denominations that accept his theology.
First the tl;dr version:
Christ's death is significant, not as redemption itself, but as the final battle in a process of redemption that took place throughout Christ's entire lifetime on earth.
Now the actual, not really tl version:
To put the cards on the table right from the start, Swedenborg utterly rejected the idea, common in Protestantism, that Christ's death on the cross was redemption, along with his rejection of the penal substitution model of atonement and of the doctrine of the Trinity of Persons. In True Christianity #132-133, Swedenborg takes up and explains this proposition:
Believing that the Lord's suffering on the cross was redemption itself
is a fundamental error on the part of the church. That error, along
with the error about three divine Persons from eternity, has ruined
the whole church to the point that there is nothing spiritual left in
it anymore.
(As was common in the theological polemics of his day, Swedenborg does not mince words!)
For Swedenborg's full argument, please consult True Christianity itself. It would take too long to present it here. But just to give a brief taste of the biblical basis for rejecting Christ's death on the cross as being redemption itself, consider this passage from Micah:
With what shall I come before the Lord, and bow myself before God on
high? Shall I come before him with burnt offerings, with calves a year
old? Will the Lord be pleased with thousands of rams, with ten
thousands of rivers of oil? Shall I give my firstborn for my
transgression, the fruit of my body for the sin of my soul? He has
told you, O mortal, what is good; and what does the Lord require of
you but to do justice, and to love kindness, and to walk humbly with
your God? (Micah 6:6-8, italics added)
The idea that the physical death of Jesus Christ could pay for the spiritual sins of humankind is contrary to scripture. And as the original questioner points out, although Christ's physical suffering on the cross was great, it was no greater than what millions of human beings have suffered throughout history. Whatever happened on the cross, it must have been primarily a spiritual struggle or passion rather than a merely physical one.
As for the idea that Christ paid the price or penalty for our sins by dying on the cross, though this is a commonplace of Protestant doctrine, it is never actually stated in Scripture. (See my article, "Did Jesus Really Die to Pay the Penalty for our Sins?!?") And as a matter of history, the penal substitution model of atonement was not a significant doctrine in any part of Christianity until the Protestant Reformation, 1,500 years after the time of Christ. Positing it as the fundamental soteriological doctrine of Christianity, a belief in which is necessary for salvation, is stating that Christianity was ineffective, null, and void for salvation throughout the first 1.5 millennia of its existence.
According to Swedenborg's theology, then, why is Christ's death significant?
As seen in the various Swedenborgian denominations, the emphasis on Christ's death in both Protestantism and Catholicism is far too great. Yes, Christ's death was important. But in Catholicism and especially in Protestantism it takes on so great a significance as to eclipse everything else that happened in the Gospels, and indeed, in the entire Bible.
Instead, Swedenborg taught that the Passion of the Cross was quite simply the final spiritual battle of a whole lifetime of battles against evil, the Devil, and hell. Through Christ's continual victories in these battles, he overcame the rampant power of hell, which had threatened to overwhelm humanity and drag all people down to the slavery of hell. By conquering and breaking the power of evil, Christ saved all of humanity (not only believing Christians) from inevitable and irresistible eternal death.
Most of what the Gospels offer us is a narrative of the outward life of Jesus, especially focusing on his ministry of preaching, teaching, and healing (to use the traditional language--see Matthew 4:23; 9:35).
However, aside from the crucifixion itself, we do get at least two brief glimpses into the inner struggles and temptations that Jesus went through during his lifetime on earth:
- His temptation in the desert after his baptism (see Matthew 4:1-11;
Mark 1:12-13; Luke 4:1-13)
- His agony in the garden of Gethsemane just before his crucifixion (see Matthew 26:36-46; Mark 14:32-42; Luke 22:39-46)
Based on these two narratives and on his frequent conflict with the worldly religious and political authorities of his day, we can understand that Jesus was also engaged in a lifelong spiritual battle "against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places" (Ephesians 6:12). This is why Jesus could already say to his disciples before his crucifixion:
In the world you face persecution. But take courage; I have conquered
the world! (John 16:33)
By that time he had nearly completed his work of conquering the worldly power of the Devil and hell. In order to complete that work, "when the days drew near for him to be taken up, he set his face to go to Jerusalem" (Luke 9:51).
The significance of Christ's death, then, is not that it was redemption, but that it was the final act of the redemption that Christ had been accomplishing throughout his lifetime on earth. It was the final battle against the power of evil, the Devil, and hell, by which Christ achieved full victory over them, and thus saved us from their damning power.
A full exposition of this doctrine of atonement and salvation would go far beyond the scope of this answer. However, there is a somewhat fuller version in my article "Who is God? Who is Jesus Christ? What about that Holy Spirit?"
Once again, this answer is given from the perspective of the theology of Emanuel Swedenborg, and of the denominations that accept his theology. It therefore represents a small minority position in the Christian world of today.
However, far from being a johnny-come-lately on the scene of Christian theology, Swedenborg's theory of atonement can be seen as a development and refinement of one of the earliest atonement theories in Christianity, known as Christus Victor, which predates the currently reigning Protestant and Roman Catholic theories of atonement by many centuries. Christus Victor and the ransom theory were the dominant views of atonement for the first thousand years of Christianity.