What does Psalm 4:8 mean?

Despite the ever-present threats against his life (Psalm 3:1; 2 Samuel 15:13–14), David enjoyed such a close relationship with God that he was able to get a good night's rest. He trusted the Lord to keep him safe. Instead of tossing and turning at night, he tossed his burdens onto the Lord's shoulders and turned his troubles over to Him. First Peter 5:7 talks about "casting all your anxieties on [God], because he cares for you." Philippians 4:6 admonishes us "do not be anxious about anything" and to instead pray with thanksgiving, making our requests known to God. The following verse promises, "And the peace of God, which surpasses all understanding, will guard your hearts and your minds in Christ Jesus" (Philippians 4:7).

Acts 12 includes the account of the arrest of the apostle Peter. King Herod fully expected to kill him the morning following the arrest. However, instead of worrying all night, Peter slept soundly while chained to two guards with sentries posted at his cell's door. His commitment to the Lord's will was so strong that he enjoyed such a deep sleep that an angel that was sent to rescue him had to strike him on the side to wake him up. Undoubtedly, a strong trust in the Lord exerts a powerful impact on the ability to sleep soundly.