The Bible is filled with paradoxes, and Paul's analogy in which he compares our human bodies to vessels/jars of clay is one such paradox.
The power of paradox is found primarily in stark contrasts and apparent contradictions. My favorite one (if you'll indulge me) comes from Jesus, and it is included in all three Synoptics:
For whoever wishes to save his life will lose it; but whoever loses his life for My sake will find it (Matthew 16:25 NASB Updated).
For whoever wishes to save his life will lose it, but whoever loses his life for My sake and the gospel's will save it (Mark 8:35).
For whoever wishes to save his life will lose it, but whoever loses his life for My sake, he is the one who will save it (Luke 9:24).
The missionary martyr, Jim Elliot, who died in 1956 (along with four other missionaries) attempting to bring the gospel to a barbaric tribe in the heart of the Amazon forest, paraphrased Jesus' statement as follows:
He is no fool who gives what he cannot keep to gain what he cannot lose.
Now, on to the apostle Paul and the pericope in question. In Paul's day, as in ours, clay was not a precious commodity. True enough, then and now it can be sculpted into something beautiful, not to mention practical, but the material itself and the ordinary vessels crafted out of clay are simply not in the same category as, say, precious or semi-precious stones.
Paul's use of contrast is clear: On the one hand you have an inexpensive earthenware vessel, but on the other hand you have a treasure of inestimable worth. The earthenware vessel is the Christ follower, and the treasure is found in verse 6 of 2 Corinthians 4:
For God, who said, "Light shall shine out of darkness," is the One who has shone in our hearts to give the Light of the knowledge of the glory of God in the face of Christ.
The "glory of God" has been defined as "the outshining of God's presence." That presence can be detected in the marvelous creation God brought into being by the word of His power. The sheer magnitude and magnificence of the physical universe we humans inhabit are mind boggling. Here is how King David described God's creatorial splendor:
The heavens are telling of the glory of God, And their expanse is declaring the work of His hands. Day to day pours forth speech . . . (19:1-2a).
We seldom stop to think of this, but space (in the sense of outer space) contains the universe, but the universe itself cannot contain God. God is beyond time and space, since he alone is an infinite and eternal Spirit.
The miracle of the incarnation of God in the person of Jesus Christ is certainly the greatest miracle God has ever performed. In close second, however, is the miracle God performs whenever a sinner comes to him by faith and receives God's gracious gifts of forgiveness and eternal life through the new birth, all on the basis of Christ's redemptive death and resurrection.
Truly, the transformation which God effects in human beings is amazing. He takes rebellious creatures who are dead in sin, and in Christ makes them new creations (2 Corinthians 5:17). Alhough the transformation is not complete at the time of the new birth, one day it will be when they are conformed in glory to the image of God's beloved Son and our Savior, Jesus Christ (Romans 8:29).
In the meantime, we fallible and finite human beings have this amazing treasure of the living Christ within us, mere clay vessels, but God is pleased to work in us and through us in spite of our weakness.
Here is where the significance of the clay jar comes in. God chooses to use humble clay jars
so that the surpassing greatness of the power will be of God and not from ourselves (v.7b)
Paul uses a similar paradox in speaking of his "thorn in the flesh" in chapter 12:7 ff. We do not know what that "thorn" was, but once Paul realized God was not going to take it away from him even after he implored the Lord three times to do so, he also began to realize the reason why he would have to live with this thorn in the flesh.
First, because of the "surpassing greatness of the revelations" God had given him in the past (v.7), the thorn would be a constant reminder to him not to give in to the temptation of exalting himself, thinking that somehow he was deserving of those great revelations. Paul did not deserve them; rather, they were a gift of God's grace, pure and simple.
Second, once Paul realized he neither deserved nor earned those special revelations, he experienced what could be called a paradigm shift in his thinking, which he summed up in this way:
Most gladly, therefore, I will rather boast about [or in] my weaknesses, so that the power of Christ may dwell in me. Therefore I am well content with weaknesses, with insults, with distresses, with persecutions, with difficulties, for Christ sake; for when I am weak, then I am strong (vv.9a-10).
Once Paul realized he was but a fragile clay jar whom God was pleased to use for his glory and not for Paul's, then and only then did he appreciate fully the treasures of God's grace. Whether that treasure was the gospel itself--the "Light of the knowledge of the glory of God in the face of Christ and the surpassing greatness of his power (chapter 4); or whether the treasure was evidenced by the miracles flowing from the gospel, such as the surpassing greatness of revelations (chapter 12); the fact remained that Paul was simply a humble--even utilitarian--clay jar whom God was pleased to use for his glory, and his glory alone.
Therein is the true significance of the clay jar: out of something so humble God is able to manifest his power, his strength, and his glory.