There are quite a few different ways of looking at this text. What is it that is "lacking in Christ's afflictions"? And, how exactly is Paul "filling up" that which is lacking?
Sam Storms does a great job of narrowing the discussion, you can read the full thing here.
The six options are thus:
- Redemptive: Paul is somehow filling up what is lacking in Christ's redemption
- Glorifying: Paul is giving more glory to Christ through his suffering
- Typological: Paul's suffering is corresponding to the suffering of Christ
- Eschatological: There is a set amount of suffering that Christians will endure, Paul is filling up that bucket of suffering with his suffering.
- Extending: Ministers, like Paul, extend the message of the suffering servant to others through their suffering in ministry. Christ is not lacking in propitiation but in presentation. Therefore, Paul is extending the presentation of Christ, through suffering, to the nations.
- Union Suffering: Paul is suffering where Jesus would have as an example and encouragement to benefit the Colossians.