What does Hebrews 12:15 mean?

SEE TO IT THAT NO ONE FAILS TO OBTAIN THE GRACE OF GOD; THAT NO "root of bitterness" springs up and caused trouble, and by it many become defiled. 

(HEBREW 12:15 ESV)

This verse continues to give practical steps Christians ought to take in response to persecution and hardship. Earlier, the writer encouraged believers to "hold fast" (Hebrew 3:6; 10:23) in the face of struggles. Most of the suffering we endures as Christian is not as heavy as it could be (Hebrew 12:4). And, God intends those experience for our good to train us into a more mature faith ( Hebrew 12:11).

While we grow individually, we also need to be careful of how we interact with other believers. The prior verse mentioned the need to live in peace, as well as the importance of pursuing holiness.

The reference to those who "[fail] to obtain the grace of God" could mean those who are false believers. That would harmonize with other New Testament warnings about those who claim to be godly, but are not (Matthew 7:15, Jude1:12). Upcoming verses tie into the example of Essay, who was careless towards his own birthright, also seen as a sign of one without real faith in God. While that's possible, the context seems mostly to focus on else: a command regarding those within the church who are defiant towards God and His holiness.

Prior verses mentioned the importance of holiness (Hebrew 12:14). And other New  Testament verses mention the importance of not tolerating brazen sin among those who claim the name of Christ (1Corinthians 5:11). Earlier, a warning in this same letter was given  to those who believe, but fail to obey and are judged accordingly (Hebrews 10:26-31). The "root of bitterness" mentioned here re-established a metaphor used in Deuteronomy 29:18-19. There, the people of Israel were warned about those who assumed they'd be blessed and protected by God, despite their willful rebellion.

It seems, then, that the writer's point is about those who are disobedient toward God. Old Testament Hebrew uses the word "bitter" as a reference to poison. Here, the"bitter roots" are said to cause trouble and defilement. Whether those person are outright false Christians, or merely rebellious believers, thei influence is the same. They cause controversy and lead others into sin . Such person cannot be allowed to remain in the body of believers (1Corinthians 5:13).