Remembering that Timothy was a minister of the church of God, the gift was the power and authority to fulfill his responsibility within it. Though this book was originally just written to Timothy, it has application for all Christians. The principles in it involve every one who has the Spirit of God. Each has been given gifts by God to carry out his portion of God's work within the body.
Salvation is more than mere forgiveness of sin. Another part of God's salvation is that he gives gifts—abilities, talents, powers, authority—to do jobs within the church. Salvation requires a journey to the end of God's purpose. It is a way of life that leads to a goal. God gives every one of us the powers to succeed in reaching the end of the journey: gifts of the Spirit given to carry out our functions within the body.
Just as the apostle Paul used the human body in an analogous way, showing that every portion of the body has its function, so has every portion of the human body been given the power to carry out that function in behalf of the body. So with God's church: No matter how scattered it is, or how unified it is, God has given each Christian the power to carry out his function within the body. So Paul prodded Timothy to make good use of those gifts to help the church.
There is no indication within the context that Timothy was falling short in any way. It is clear from the verbal forms that Paul uses here that these were things that Timothy had done in the past and was continuing to do in the present. It could really be written more accurately in the English, "keep fanning the flame." He was stirring the gift, and Paul was saying, "Keep on stirring it!" Timothy was cultivating the doctrine, the major means by which one keeps or guards what has been given.
