"but it has now been revealed through the appearing of our Savior, Christ Jesus, who has destroyed death and has brought life and immortality to light through the gospel." NIV translation
Paul continues to remind Timothy that our salvation through grace had been hidden but was made apparent to all by the "appearing of our Savior". This is speaking of the resurrection of Jesus Christ which is the foundation of the gospel (good news). Why is that fact the foundation of the gospel? Jesus had promised that He would be raised from the dead and that we would as well. If He had not been seen alive after His crucifixion, then, that would have been a lie and we would be without any hope.
He goes on to remind Timothy that, because of the fact that Jesus was raised from the dead, we can be assured that death has been defeated and we see that mankind has been made immortal. Even today, there are many people that believe that our life in this body on the earth is all that there is and, after it is over, we just cease to exist. The fact that Jesus walked the earth again even after he had been physically dead shows us that we do, in fact, live forever.
That brings up the question of who lives forever and whether it is all men or just those that believe in Jesus and we see the answer in the fact that Paul does not say that it is for believers only.
Why does Paul go into this topic in this his final letter to Timothy and the rest of the Christian world? God had revealed to Paul that Timothy was going to have to make a choice of whether to be bold and stand up against idolatry or to let it pass. Timothy was known for being quiet and somewhat timid but, by reminding him of the fact that we will live forever with Jesus, He was hoping to prepare him to make the right choice.