In his second letter to Timothy, Paul encourages him to be unashamed of the gospel and of Paul, who is incarcerated for the sake of the gospel in Rome.
What can I learn from this?
Being a mother, of course I love verse 5, which says, "I have been reminded of your sincere faith, which first lived in your grandmother Lois and in your mother Eunice and, I am persuaded, now lives in you also." It is a great encouragement to me that the sincere faith of a parent may be passed on from one generation to the next. Of course, this doesn't occur automatically, rather it comes through God's responses to the intercessory prayers and teaching of the parents (cf 2 Timothy 3:14-15).
Paul's focus in this passage is on encouraging Timothy, who, Paul knows, has been deeply saddened by what has happened to Paul (in v4 Paul remembers Timothy's tears.) Paul wants Timothy to be unashamed of the gospel and to live in the power of God that comes through that same gospel. Paul writes in verses 7-9a, "For God did not give us a spirit of timidity, but a spirit of power, of love and of self-discipline. So do not be ashamed to testify about our Lord, or ashamed of me his prisoner. But join with me in suffering for the gospel, by the power of God, who has saved us and called us to a holy life - not because of anything we have done but because of his own purpose and grace." This statement seems quite radical in its view of suffering as being undergone on the behalf of the gospel. Not only that, but the suffering is undergone with strength through the power of God - to uplift one's spirit from timidity (cowering meekness) to love and self-discipline (self-control).
Paul's reasoning behind this is that, whatever the deeds of men in fighting against the gospel of Jesus Christ and His apostles who share that gospel, this teaching is "sound," a "good deposit" within believers. It is worthwile undergoing many pains because Jesus Christ is trustworthy and we have a sure hope of eternal life through Him.
How can I apply this to my own life?
This is one of those passages to store up and remember so that, in times of trials, I may return to it and be encouraged. Paul wrote this in the last period of his imprisonment in Rome, I think this letter is though to be his last (extant). Yet Paul displays a faith in God that is seeing him through his trials. I pray that, if the time comes that I may experience bitter persecution in my faith, I may follow the example of Paul and be encouraged, like Timothy, to hold firm to the faith that I have received