To me, for Paul, that meant accepting his share of sufferings, giving himself daily for the cause of Jesus and for the sake of fellow believers. Press on… it should be a constant inspiration to become a more faithful disciple of Jesus. What does it matter if we have failed? What does it matter if we feel discouraged at times? Those are the times to PRESS ON! Pressing means going beyond the comfortable limits, the easy victories, into the uncharted path known to but few.
That is one issue we today suffer… that is creature comforts. And by doing so, we lack being more faithful disciple of our Lord Jesus. But once we begin to truly suffer, be it an illness, loss of job, etc, we begin to pray, and get closer to God. Hence, we Press On to Jesus.