I'm a huge fan of Colossians Remixed by Walsh and Keesmat. They comment:
'it would seem Paul is saying that identification with Jesus, and specifically being his body in a world that is still hostile to his rule, means that the church will experience affliction. That's what it means to be the body of Christ. Further, Paul's own afflictions - remember, he writes thee epistle from prison (Col 4.18)! - are for the sake of the body, for the sake of the church...
'Perhaps a better translation here is "in my flesh I complete what is lacking in the oppression of the Messiah, for the sake of the body, that is, the church." Insofar as the Messiah, as the representative of the people, was oppressed, so Paul in his suffering is also oppressed for the sake of the Messiah's people, the church, for whom he has become a servant (1:25)...
'Paul weaves together the oppression of the Messiah and the oppression he is experiencing in his imprisonment at the hands of the empire, so that his afflictions are identified with the Messiah's and are therefore redemptive for Christ's body, the church...
'for those of us who live at the heart of the empire, this all raises a very uncomfortable question. If, as Paul asserts through his letters, we are called to share in the sufferings of Christ, and if such suffering is for the sake of the body of Christ, where does that leave a Christian community that seems to avoid any soft of suffering? Where does it leave thsoe of us whose lives seem to be blessed by the empire rather than threatened by it? Where does it leave those of us whose blessings seem to actually be dependent on the oppression of our brothers and sisters elsewhere?'
pp. 228-230

I think this is part of Paul's understanding of what it is to be an apostle.

Does Paul's understanding of his own suffering bear any relation to the theology of Isaiah's Suffering Servant? "By his stripes we are healed". That representative (?) figure is identified by some Jewish readers as combining the suffering of Israel and the suffering of God's prophet. There the servant's suffering is connected with the people's hope of healing and restoration. Over the years this has also been applied by many Christian interpreters to the sufferings of the Messiah and their eschatological significance (in the fruits of which both the church and the gentile world share).

So is Paul extending that historic family of messianic suffering to include his own sufferings on behalf of the body of Christ? Eschatologically the salvation won through Christ's sufferings is extended to more and more peoples as the church continues to grow through the sufferings of its apostle(s). In this way the work started by Christ is carried on by his messengers as they share in his sufferings - or even add to them.

It's a very Paul-centred view of suffering (me and the Lord are doing this for you). It tends towards placing Paul and his sufferings in a representative role (though not a soteriological one -what is lacking in Christ's sufferings is their application to new peoples, not that they are insufficient and have to be topped up by others!). But however this all seems to us, it may have been one of the things Paul told himself to keep going in the face of opposition and hardship. And one of the things he told the churches so they'd be encouraged by his sufferings and not ashamed of them.

You get other glimpses of this sort of thing in Paul's statements about his sorrow being for the joy of the churches (is that in Corinthians?) and in Philipians 3 and his desire to know Christ and to share in his sufferings.

Sorry, you asked for plain English!

Paul suffers as he does his work of evangelisation and church building. The more Paul's body fills with affliction (imprisonments, mob violence, stonings, shipwrecks, etc.), the more Christ's body the church benefits. The more Paul suffers the more the church grows.

So in some mysterious way, that's continuing the work Christ started on the cross and Paul's quite happy about that.

Thanks Simon, Andy and Sean (via email) for these.

I think the answer is, based on what you've all said/share that you can't have the answer in plain English because you have to interpret it through the lens of the church as the body of Christ (I have no problem with that). I'm still not quite sure that without a lot of time and contemplation I can work through what that means in practical/contextual theology terms... that is the 'so what' for local congregations living relatively charmed lives in liberal western democracies. That will have to be someone else's PhD!