In the New Testament, sometimes the imposition of hands is done in connection with baptism, and sometimes it is done in the act of ordaining. It is pretty universally related to the conferral (or strengthening) of the Holy Spirit on a person.
Timothy we know was made bishop of Ephesus. The references to the imposition of hands on him are clearly in the context of his episcopacy:
Till I come, attend to the public reading of scripture, to preaching, to teaching. Do not neglect the gift you have, which was given you by prophetic utterance when the council of elders laid their hands upon you. (1 Tim 4:13-14)
Baptism generally doesn’t involve a “council of elders” laying hands on the baptized.
As bishop, he acts in the ordaining of others; thus:
Do not be hasty in the laying on of hands, nor participate in another man’s sins; keep yourself pure. (1 Tim 5:22)
It seems reasonable, then, that 2 Tim 1:6 refers to the imposition of hands related to his ordination. This is confirmed by commentary on this verse from St. John Chrysostom:
“I put thee in remembrance that thou stir up the gift of God, that is in thee by the putting on of my hands,” that is, the grace of the Spirit, which thou hast received, for presiding over the Church, for the working of miracles, and for every service. (Chrysostom, Homily on 2 Tim 1)
The Council of Trent used this verse in defending the sacrament of Holy Orders:
Whereas, by the testimony of Scripture, by Apostolic tradition, and the unanimous consent of the Fathers, it is clear that grace is conferred by sacred ordination, which is performed by words and outward signs, no one ought to doubt that Order is truly and properly one of the seven sacraments of holy Church. For the apostle says; I admonish thee that thou stir up the grace of God, which is in thee by the imposition of my hands. For God has not given us the spirit of fear, but of power and of love of sobriety. (Session XXIII, Chapter 3)