What does this passage mean?What you have to ask yourself is this: What could still be lacking in the sufferings of Christ? He suffered to the fullest extent, and for all mankind. This work is called the objective redemption, and the degree, or quality, or completeness of it has no imperfection.
Col 1:24-25 Now I rejoice in my sufferings for your sake, and in my flesh I complete what is lacking in Christ's afflictions for the sake of his body, that is, the church, 25 of which I became a minister according to the divine office which was given to me for you, to make the word of God fully known,
At a glance, one might think this means Christ's afflictions are lacking. I don't believe that, but I don't know what it means.
But, there is still something lacking. What is still required is the application of the grace of the Cross upon us. He won all the grace through his perfect suffering, but this grace must still be applied to us. This application is called the subjective redemption. We know that it is necessary b/c if it wasn't, then everyone would have been instantly saved as soon as Jesus said, "It is finished." But, we're not.
So, we have thus far established what is lacking. Now, Paul tells us in this passage that one way to make up for what is lacking is by suffering, by taking up our Cross just as Jesus Christ took up His. Suffering for the body is meritorious. It is a good deed, and all good deeds done in grace serve to build up the Body of Christ.
This explains why Paul would rejoice in his sufferings, and see this as something that he did for their sake (cf. Col 1:24). He knows that when he suffers for the Gospel, to fulfill the duties of the "divine office" given to him (cf. Col 1:25), he builds up the Body of Christ and becomes a minister of the grace that flows from the Cross. Elsewhere, Paul says, "Therefore I endure everything for the sake of the elect, that they also may obtain salvation in Christ Jesus with its eternal glory" (2 Tim 2:10). Everything that Paul says in his letters about the redeeming value of suffering affirms this understanding of Col 1:24-25.
I hope that helps.