In this verse, the writer identifies the letter's recipient and offers a standard Pauline greeting. The letter was written to Timothy, one of four personal New Testament letters by Paul. The reference to Timothy as "my child in the faith" indicates a spiritual relationship, most likely the result of Paul leading Timothy to faith in Christ. Only Timothy and Titus were called "true children" by Paul. 
In addition to teaching unbelievers the truths of the gospel of grace, Paul stressed the importance of nurturing, disciplining, and encouraging baby believers to grow in the faith. Justification, in God's eyes, is a once-off event, whereas sanctification is a lifetime process. It is essential for all believers, especially new Christians, to receive the right type of teaching in order to develop into healthy Christians. 
Throughout his letters, Paul provides great encouragement and edification for each of God's children. Also included are authoritative instructions on living the Christian life, as well as a method for identifying and combating false teachings. Further, it provides us with the blessings of God's grace, the joy of His mercy, and His perfect peace.

Dear Heavenly Father, You have bestowed grace, mercy, and peace on all Your children who walk in humility, gentleness, and desire knowledge of the truth. Thank You for making me Your child through faith in Christ Jesus. Let me die to myself so that I can live for Him alone. Thank You for allowing Paul and the other apostles of Christ to serve You. In the evil days, may I stand firm and grow in grace and knowledge of our Lord and Savior. 
In Jesus's name I pray. Amen.