From the context - and from the similarly-worded description of Epaphras in 4:12 - it's clear that Paul is speaking about his prayers for them.
He's in prison, let's remember, so he can't be referring to very much by way of other types of activity on their behalf. And somehow I don't imagine he has in mind writing letters to the emperor or to the local authorities in Colossae and Laodicea to petition for the believers there. You might say he at least means the letter he's writing to them - after all, that's a form of ministry that probably wasn't dashed off before an afternoon siesta - and instructing Tychicus before he goes back to them. Well, maybe he would include those - but there's so little doubt as to what he really means. He's speaking about his prayers for them - prayers that have been reported on, briefly, in 1:9ff.
This praying, this interceding - and let's not forget it's for believers he's not yet met - comes under the heading of hard work. He's contending for them in his prayers - taking their side, pleading for them, wrestling for them. It drains him. He suffers in doing so. This isn't a few pleasant and polite requests; it's hard work, it's demanding labour. It's warfare.
Not because the one to whom he prays is a reluctant hearer of prayer. That's not the case at all. No, the intensity is because of the significance of the issues for which he prays - the maturing of the believers into fully-assured and fruitful Christians, who won't be deceived by fine-sounding arguments or taken captive by hollow and deceptive philosophy. And because there are all manner of obstacles being put in the way of that, both seen and unseen, whose only intent is to harm and destroy the church.
The content and the contention in Paul's prayers is a continual rebuke to my own. But they also provide a model and a framework for me, for us, to embrace and to get down to work with. These are surely days in which we need to be contending hard in prayer for the Lord's people, both near and far.