Peter T. O'Brien on Philippians 1:12-26 from The Epistle to the Philippians (NIGTC; Eerdmans, 1991):
For Paul the goal of the gospel's advance overrides all else; thus his personal inconveniences, sufferings, and imprisonment serve this end. He knows of this surprising progress of the gospel because of the effects of his imprisonment upon those outside the Christian community (v. 13) and because others within the Christian fellowship have been given fresh courage for the work of evangelism (v. 14)...Paul knows of the progress of the gospel through these empirical results (vv. 13-14). Their presence shows the gospel is making headway at Rome. At the same time one can describe these results as the advance of the gospel itself, or at least significant elements of its progress (87, emphasis mine).
My guess is that most of us don't typically tend to think of our personal inconveniences and sufferings in light of how they serve the goal of the advance of the gospel.