From the beginning of the Christian movement the church has struggled with the issue of "lapsi". The Lapsi are those who professed faith in Christ, lived as Christians and then, for whatever reason, either left the faith or returned to their previous religion. At the writing of Hebrews this has become a struggle in some areas. In particular, for the writer of Hebrews, are the "jewish-christians" who are making the choice to return to more traditional judaism. In the time of Constantine and later there is always the issue of restoration of those who denied Christ while under duress or persecution and later want to be restored to the community. The Christian church has traditionally made space for them and, after a season of penance and reflection have welcomed them home.
The point that the author of Hebrews makes is that it is difficult for them to come back. Once we trust Christ for our salvation and then turn away from him there are many difficulties in returning to faith in Christ. In verse 6 the author suggests that these people are "crucifying Christ again . ." in other places we find references to dogs returning to their vomit and pigs returning to their slop. Strong language, indeed. But there is peril in "falling away." How do we live the truth, leave the truth and again live the truth. Most faithful Christians have had this experience on some minor way. Most faithful Christians can point to times and seasons when they were not living very "Christ like". Most faithful Christians, if they did not "fall away", have certainly seen the path that leads that way and have certainly struggled with being fully faithful.
The author concludes the discussion with a reminder that God's promise is certain (see 13-20) using Abraham as the primary example.