Paul's warning to the Hebrews here is a bit stronger than what he says in Philippians 1:27. He says there, "Let's all with one mind strive together to keep the faith of the gospel." Here he says, "Give earnest heed to the doctrine, to the gospel, to the things we heard, because we're in danger of losing it!" He feels he must frighten them, saying, "Don't you remember that under the Mosaic dispensation people were punished very severely for neglecting what they had heard? Every transgression and disobedience received a just reward. How much greater under the dispensation through Christ, the Son?" He is quite serious. Work hard. Be diligent. Make your calling sure!
It is about this same time that Peter and Jude add their voices to his. The brethren were undergoing a rough time because false ministers and false teachers were in the church, and like us, they also had to fight off the pressures from the world to conform. It takes great effort to resist both in the church and out in the world. When there are problems among us, it is tough. When we must also resist all the downward pulls outside in society, it is a difficult, sore trial. Thus, Paul uses particularly strong language to motivate them to stand up, face the problem, give it their all, and vanquish it.
Are we in a similar circumstance? Perhaps some of the details are different; the deception has taken a somewhat different form (this time we do not have to contend with Gnosticism, per se). However, there is enough similarity that warnings here, as well as in the books of Peter, John, and Jude, make a lot of sense. Certainly the results, the fruit of false teaching, are the same: apostasy, falling away, confusion, distrust (especially of those who have been given a measure of authority, the ministry), scattering, and disunity. The apostles, then, are speaking to us.