Paul begins his message to Timothy in this verse by issuing a warning. First, Paul refers to a time period known as "the last days." This is not necessarily a reference to an era of the distant future but rather a period of time that began with the dawn of the church age and continues today. As a second point, these last days will be challenging. 
In Paul’s remarks to Timothy, he reminds him of how his family raised him in the faith and then of how Timothy served faithfully with Paul in the past. Paul then emphasizes two primary points: To begin with, Timothy's background in the faith should give him the courage to stand firm in His faith during difficult times. The second point is that Timothy should make use of his courage to defend the gospel message's truth. 
In today's world, we are much closer to the return of Christ than the disciples in those early days of Christianity when the perilous times began. Nevertheless, men and women have read and understood this passage and faithfully carried out Paul's last instructions to the Church throughout history. Likewise, may we fulfill our responsibilities to God and to our fellow man with steadfast faith in Jesus.

Dear Heavenly Father, You have provided wisdom and warnings in Your Word. Thank You for this gift. Please keep me from going in the same direction as people around the world in these perilous times. As I follow the instructions of Paul, I will look towards Jesus, the Author and Finisher of our faith, and I will seek in the power of the Holy Spirit to live in these increasingly perilous times as Paul instructed, to Your praise and glory for all eternity. 
In Jesus's name I pray. Amen.