What does Mark 13:11 mean?
Luke 21:14–15 words this a little differently: "Settle it therefore in your minds not to meditate beforehand how to answer, for I will give you a mouth and wisdom, which none of your adversaries will be able to withstand or contradict.". Jesus basically says not to try to figure out beforehand how to make a defense before these kings and governors. The Holy Spirit will give such a defense that adversaries will not be able to contradict it. Of course this doesn't mean we won't face persecution, just that the persecution won't be justified.The equipping of the Holy Spirit acts as a witness to others of the reality of Christ. When Stephen was first confronted before his arrest, his enemies "could not withstand the wisdom and the Spirit with which he was speaking" (Acts 6:10). When Peter and John were brought before the Sanhedrin and gave their testimonies, the council had a hard time believing such "uneducated, common men" could speak so boldly; "and they recognized [the men] had been with Jesus" (Acts 4:13). It is this God-sent power that equipped the prophets (Hebrews 1:1), and although we do not have new revelation to express, as the Old Testament prophets did, we can still rely on the Holy Spirit to help us spread the good news of Jesus.
Nor does this mean we shouldn't prepare our knowledge at all (1 Peter 3:15), only that we don't need to obsess about those particular moments. Being confident in the Holy Spirit doesn't mean being carelessly unprepared. The apostles prayed for boldness in the first days of the church, that they would be able to evangelize despite the threats (Acts 4:29–31). Paul, despite his natural forceful personality, asked for prayer that he would continue to be bold and not afraid (Ephesians 6:19–20). The prayers worked, and Paul was even able to give his defense under heavy persecution (2 Timothy 4:17).
One of the major themes of Mark 13 is that we need to watch in order to be prepared. Not that we have all the details worked out, but that our hearts are ready for whatever challenges we will face, whether that be false teachers (Mark 13:5–6), natural disasters (Mark 13:8), or the chance to share the gospel before we're executed.