What does Mark 9:44 mean?

This verse is not found in the oldest and most reliable transcripts. When it is included, it and verse 46 are identical to Mark 9:48. It's possible that this phrase was added by a well-meaning copyist trying to harmonize each statement. Jesus quotes from Isaiah 66:24 which describes the fate of sinners facing God's final judgment.

Jesus has just said that it would be better to cut off your hand and have eternal life than to have two hands yet enter hell. In the following verses, He will say the same about cutting off a foot or tearing out an eye. The sentiment is a traditional way of saying that we should use any needed measure to prevent specific sin.

The idea is somewhat uncommon in today's culture. Discipline is lauded as a method to make money, get in shape, or master a new skill. The world is less interested in setting up boundaries to avoid sin.

In contrast, the Jewish scribes excelled at setting "fences" around God's law so that people wouldn't even come close to sinning. They codified these fences in the Oral Law. The Pharisees were experts at following those extra rules.

Jesus responded by pointing out that truly obeying the Mosaic Law was hard enough without all these specific, manmade additions. Obeying the spirit of the Law would be difficult enough: Don't just avoid murder, avoid anger (Matthew 5:21–22). Don't just avoid adultery, don't let yourself be tempted at all (Matthew 5:27–28). Go even further in the work of loving others by submitting to the needs of those who cheat and abuse you (Matthew 5:38–48). If you want to earn heaven, be perfect.

Of course, none of us can be perfect. And so Jesus came and died for our sins. It is good to try to obey God's will and His commands. It is better to also realize we will never do so perfectly, and we need God's grace.