This is an interpretation from a Catholic site. We actually discussed this verse several weeks back and what it means:
Christians believe that Jesus' suffering and death were entirely sufficient to forgive all the sins of the world. Why, then, does Paul say that Christ's afflictions are lacking something? How can this possibly be? The question can only be answered by the 2,000 year-old Catholic understanding of how we as Christians participate in Christ's work of redemption and salvation.
Most Protestant churches leave you pretty unfulfilled when they teach about suffering. Because in Protestantism all you generally need to do is accept Jesus as personal Lord and Savior to be saved and nothing more, suffering is simply viewed as something we must endure as part of the human condition, without any value or merit for ourselves or others. Because the Catholic Church believes that each of us, by virtue of our baptism, participates in Christ's eternal priesthood, she instead teaches that our prayers, works, and even suffering further Christ's work of redemption. This is the necessary effect of belonging to the communion of saints. This is also what Saint Paul is writing about in Colossians 1:24.
In the verse, Paul says he rejoices in his suffering for the sake of others. Knowing what we know about Paul, we can safely conclude that he would not rejoice in anything, much less write about it in a theological epistle, unless it brought about Christ's work of redemption. We also see that Paul's rejoicing is not for himself, but for the other members of the Church. So Paul's rejoicing about the value of his suffering in the work of redemption is based on his understanding that his suffering is helping others (it is not because he enjoys the pain of suffering). This becomes clearer as Paul explains his teaching in the context of the Mystical Body of Christ, for, only in this context can Paul's teaching make sense.
Paul explains that he completes what is lacking in Christ's afflictions. But Paul does not do this for the sake of Christ Himself, because Christ's afflictions were sufficient and perfectly efficacious for our redemption. Paul could add nothing to the power of Christ's sufferings. Instead, Paul explains that he does this for the sake of the Church (the Mystical Body) of which Christ is the head. Why? Because God wills us to participate in Christ's sufferings in order to further the work of His redemption. Thus, in the Church and for her benefit, Jesus Christ, in a very mysterious way, leaves room to allow our suffering to be united to His, to accomplish the will of the Father. It is by virtue of our baptism, in which we become sons in the Son and share in His priesthood, that our suffering can further Christ's redemptive work. This is lofty stuff, but it is as true as God's love for us, and it is precisely because of God's love for us.
How do we, like Saint Paul, complete what is lacking in Christ's sufferings for the sake of the Church? We offer up our suffering as a sacrifice of praise to God. Instead of just enduring the suffering, we literally will the suffering through prayer to bring about Christ's work of redemption. This is what the Church calls "redemptive suffering." This type of suffering is what Paul is rejoicing about, and this is why the way we handle suffering is so important. Such suffering can benefit not only those who suffer, but all the members of the body. The worst kind of suffering is wasted suffering. Only the Catholic Church, for 2,000 years, has both taught and lived Saint Paul's teachings on suffering.