What does Luke 11:28 mean?

Jesus is explaining how He is distinct from Satan. He does not do miracles in Satan's power; He will destroy Satan's kingdom; those who follow one cannot follow the other; those who do not choose a side will be claimed by Satan (Luke 11:14–26). A woman interjects to pronounce blessing on Jesus' mother (Luke 11:27). Here, He explains that even His closest family member, His mother, must make that choice.

This teaching of the importance of hearing and doing God's Word is scattered throughout the Bible. In several places, God tells the Jews that He values obedience over sacrifice or feasts (1 Samuel 15:22; Hosea 6:6; Psalm 40:6–8; Isaiah 1:13–17). He would rather have repentance than burnt offerings (Psalm 51:17). God's blessings to the Israelites were dependent on their obedience to the Mosaic law (Leviticus 26; Deuteronomy 28).

None of those imply that good works are necessary for salvation. Eternal redemption is always by grace through faith (Romans 4:1–8; Ephesians 2:8–9). Rather, good works naturally follow from salvation (Ephesians 2:10). To trust in Jesus is to rely on Him and seek to obey Him (John 15:1–17; Romans 6—8; 1 John 1:8—2:6). The indwelling Holy Spirit transforms the hearts and minds of believers (Romans 12; Galatians 3:1–9; Ephesians 1:3–14; Philippians 2:12–13). In the context of this chapter, hearing the word of God and keeping it means hearing the evidence that Jesus is Savior and accepting that truth. That's something even Mary had to do.

In the next segments, Jesus continues to explain that obedience to God includes believing what God says. This is what the formerly pagan people of Nineveh and the Queen of Sheba did (Luke 11:29–32). If they believe Jesus' message, given to Him by God the Father (John 12:49), they will shine with light and truth (Luke 11:33–36). If they don't, they may look good on the outside, but inside they are filthy tombs continuing the tradition of murdering God's prophets (Luke 11:37–52).