What does Luke 10:38 mean?
Twice, Jesus has told His disciples to enter towns, find a host who welcomes their message of the kingdom of God, and stay in that host's home. If no one accepts their message, the disciples are to leave while giving a sign of judgment against the town (Luke 9:4–5; 10:5–11). Luke gave an example of the latter; a Samaritan village refuses to host Jesus "because his face was set toward Jerusalem" (Luke 9:53). That is, He affirmed that the God they should worship is the God of the Jews and that He established right worship in Jerusalem, not the altar built in Samaria. When they rejected the message, they rejected Jesus and His blessings.The story of Mary and Martha gives more nuance to the conversation. Martha appears receptive to Jesus' message. She invites Jesus to her home, and He accepts. The issue is that her priorities are unbalanced. She gives more weight to hosting Jesus than listening to Him (Luke 10:39–40). Mary submits entirely to Jesus and His message.
Martha bases her actions on the culture of her era, where hospitality was among the most important social expectations. Further, in that culture, women were expected to serve, not to learn. Some traditional Jewish writers suggested women shouldn't be taught to read at all, because women learning to read the Torah would be useless and dangerous. Mary senses that Jesus is not a traditional rabbi, however, and wants to know her true place in God's kingdom.
The Christian life is similar. Once the Holy Spirit makes His home in us, He will not leave. That doesn't instantly adjust our priorities into proper focus. We can echo Martha's well-meaning error, spending too much energy on the external, simplistic aspects of welcoming Jesus. That can include exceptionally good things, such as serving at the church, listening to Christian radio, or hanging verses on our walls. But those exercises don't replace listening to His message and building a relationship with Him. Modern "Christian Culture" can be as distracting and burdensome as Martha's hospitality culture. As Paul says, such things are lawful, but they are not all helpful (1 Corinthians 6:12).