What does Psalm 41:10 mean?

The context for this comment is David's experience with his enemies. They plot for his doom (Psalm 41:5–9), but David is confident that God will forgive his sins and prevent the enemy from winning (Psalm 41:1–4). David knew he deserved punishment for his sins (Psalm 41:4), yet he also knew the Lord is gracious. God's mercy and grace both factor into His treatment of repentant believers. In His mercy, He withholds what the believing sinner deserves, namely punishment. In grace, He gives what the believing sinner does not deserve, namely forgiveness.

Ephesians 2:4 describes God as "being rich in mercy." Verse 8 declares, "For by grace you have been saved through faith." If it were not for God's mercy and grace no one would enjoy a warm, eternal relationship with Him. But mercy and grace bring those who believe on Jesus into an unending, redeemed relationship with Him. Instead of spending eternity in hell, every saved person will live eternally in heaven (John 3:16–18, 36).

Part of David's request is that he might "repay" his enemies. In this context, this means to give them their just, deserved consequences for sin.