Hebrews 13:17-19 meaning

Earlier in this chapter, the Pauline Author asked his readers to remember those who had led them and to imitate their faith. Now he asks them to obey their current leaders. Obey your leaders and submit to them, for they keep watch over your souls as those who will give an account (v 17). His readers were facing trials and temptations to leave their faith behind, but the Pauline Author asks them to obey their leaders and submit to them so that they remain faithful.

Those who were leading them were charged by God to keep watch over them and help them remain faithful and must give an account of their leadership to God. Let them do this with joy and not with grief, for this would be unprofitable for you (v 17). These believers could make the job given to their leaders much more difficult, which would not be profitable for anyone.

The Pauline Author requests that these believers pray for him as he has conducted himself with a good conscience. Pray for us, for we are sure that we have a good conscience, desiring to conduct ourselves honorably in all things (v 18). 

He has lived a life of faithfulness in service to God and hopes they will recognize that he, like their leaders, desires to conduct himself honorably and is trying to help them remain faithful: And I urge you all the more to do this, so that I may be restored to you the sooner (v 19). He wants them to pray so he may see them soon, implying that he already knew this group of believers. The Pauline Author's point is that he, and their leaders, are trying to obey God and remain faithful, and his audience should remain faithful and pray for them.