What does 1 Timothy 2:3 mean?

The idea Paul is calling "good" here is the concept of prayer from verse 2. Paul has called for prayers for all people (1 Timothy 2:1), including kings and governing leaders (1 Timothy 2:2). This is a beneficial act which Paul wants to see Timothy include in church worship gatherings. The word translated "good" can also be understood as "noble," giving distinction and dignity to corporate prayer for governing leaders.

This kind of prayer is also "pleasing" to God. The Greek word apodekton refers to something acceptable, agreeable, or welcoming. It is not merely pleasing to Paul, but also in "the sight of God our Savior." Paul also uses the phrase "God our Savior" in 1 Timothy 1:1, and three times in his letter to Titus (Titus 1:3; 2:10; 3:4). The phrase is usually associated with a command and highlights the authority of Paul's instruction regarding prayer in this context. All four of Paul's other mentions of this phrase for God include reference to a command, doctrine, or God's kindness.