What does 1 Timothy 4:10 mean?
Paul continues the instruction he began in verse 6. The end goal being fought for is godliness, or godly living, as described in verses 7 through 9. Paul and Timothy both focused their lives on spiritual growth that led to godly living. Rather than accepting false teachings (1 Timothy 4:1), or silly myths (1 Timothy 4:7), a church leader is meant to focus on knowing and defending the truth (1 Timothy 4:8–9)."Living God" was a name often associated with God the Father in the Old Testament. For example, Psalm 42:2 says, "My soul thirsts for God, for the living God. When shall I come and appear before God?" Yet this verse also calls this "living God" the "Savior of all people." Paul acknowledged Jesus and the Father as one (John 10:30).
The phrase "Savior of all people" is unique in the Bible to this verse. It clearly does not mean every person is saved in the sense that every person goes to heaven. Scripture often presents the need for people to be "saved" in order to have eternal life, rather than eternal destruction (John 3:16–18; 2 Thessalonians 1:9). The more reasonable interpretation is that Paul means to highlight the unity between Jew and Gentile (1 Timothy 2:1). Paul was encouraged by the fact that Jesus is King of kings and Lord of lords (Philippians 2:9–11), the same ruler over all people and for all time.
"Especially of those who believe" simply places an emphasis on Jesus as Savior to believers, though He is also the one, true God.