Hebrews 12:15
looking carefully lest there be any man who falls short of the grace of God; lest any root of bitterness springing up trouble you, and many be defiled by it;
WEB
Looking diligently lest any man fail of the grace of God; lest any root of bitterness springing up trouble you, and thereby many be defiled;
KJV
What Hebrews 12:15 means
It is a warning to a whole community to watch over one another, so that no one drifts away from God's grace and no bitterness takes root and spreads to poison the rest.
This comes near the end of the letter to the Hebrews, written to a group of Christians who were tired, under pressure, and tempted to give up. Just before this, the writer told them to pursue peace with everyone. Here he hands them a job to do for each other.
"Looking carefully" translates a word about watching over, the same idea as keeping a careful eye out. The writer wants the whole group to look after one another, so that no one slips away without anyone noticing.
The first danger is that someone "falls short of the grace of God." The original Greek pictures a person falling behind and being left out of reach of a gift that is right there for them. Grace is God's kindness, freely given, and the worry is that a person drifts away from it and misses it.
The second danger is "a root of bitterness." This picks up an old warning from Deuteronomy, where Moses cautioned Israel about anyone among them whose heart turns away from God, describing it as a poisonous root springing up. So bitterness here means more than a sour mood. It is a turning away that, once it settles into someone, grows like a weed with poison in its roots.
The point about a poisonous root is that it does not stay put. "Many be defiled by it." One person's turning away troubles the people around them and spreads. That is why the writer makes watching out for each other a job for the whole community.