What does Psalm 3:6 mean?

This expresses intense confidence on the part of David. That is remarkable, since the reference to "many thousands of people" is not symbolic. David's own son, Absalom, considered sending an army of 12,000 men tasked only with killing David (2 Samuel 17:1–3). The influence of David's friend, Hushai, was the only reason this plan was not enacted (2 Samuel 17:15–16). Absalom's army still pursues, but now David has time and space to prepare. Prior verses in this psalm reflect David's confidence in God, based in part on his prior encounters with death and danger (Psalm 18:3–6; 1 Samuel 17:43–47).

Being confident of the Lord's protection led David to say, "I will not be afraid of many thousands of people who have set themselves against me all around." The Bible contains many exhortations to fear not. After Abram refused the rewards the king of Sodom offered him for rescuing the hostages that had been taken from Sodom, the Lord told Abram: "Fear not, Abram, I am your shield; your reward shall be very great" (Genesis 15:1). If the king of Sodom felt insulted by Abram's refusal to accept what he offered, he might have planned to attack Abram. However, the Lord was a shield of protection for Abram, and his reward far outweighed what the king of Sodom offered.

When the ship carrying Paul to stand trial in Rome was being tossed violently by a tempest, Paul brought a message of hope to all onboard. He said an angel of God had told him, "Do not be afraid, Paul; you must stand before Caesar. And behold, God has granted you all those who sail with you" (Acts 27:23–24). There is nothing to fear if God is our shield.