"Recalling your tears, I long to see you, so that I may be filled with joy." NIV translation
Paul continues by remembering the last time that he had seen his "son" and the tears that Timothy had shed as he watched his mentor go on without him. This is a sad note as you can almost feel Paul's yearning to see him before he is executed. This verse reminds us that there comes a time in the life of a Christian when they must live out their own faith much like a young bird being forced to leave the nest and fly.
"I am 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." NIV translation
In Acts 16:1, we were introduced to this Christian family from Lystra which would have been located in the modern country of Turkey. Timothy's mother and grandmother were Jewish believers while his father was a non-believing Greek.
Paul speaks of his "sincere" faith and it brings to mind the question of what that is talking about. With Timothy's Greek father, he would have been familiar with the way that Greeks were known for their great talkers (philosophers). They would do a lot of talking but actually back it up with very little action. Here, Paul is commending Timothy, as well as his mother and grandmother, for the fact that they did not only talk a good faith but their belief was backed up by their actions.
Many times, people get this concept of actions and faith confused and it becomes more of a "religious" thing where the actions come as part of the process of being saved instead of being a result of salvation as it was with Paul and Timothy. A sincere faith in the completed work of Jesus Christ will cause us to be thankful and want to put it into action while the opposite of a sincere faith is a hypocritical "faith". A "hypocritical faith" is a false faith and speaks of one that just pretends to have faith in the work of Jesus Christ. They usually perform many "religious activities" to hide the fact that they do not really trust in the finished work of Jesus Christ.