Much has been written about today’s gospel passage (Mt 16:13-19) as it relates to the special role of Peter and his successors as Vicars of Christ. Rightfully, Mt 16:18 is the go to verse (not the only one, of course, but the primary one) for apologetic purposes against those who question or attack the institution of the papacy with Peter (reams have been produced on this, but here is one helpful resource).
Rather than go over that here, though, I would like to focus on the “key” to the Church established by Christ and how it ties in with Peter and the apostles. The Vatican II document Lumen Gentium tells us that “the Eucharistic sacrifice…is the fount and apex of the whole Christian life” (11; also see CCC 1324). We also remember Jesus’ promise, “I am with you always, until the end of the age” (Mt 28:20). Our Lord fulfills this promise through His presence, Body, Blood, Soul, and Divinity, in the Eucharist. And He has ordained that this gift only comes to us at Mass through the hands of His priests, who were ordained by bishops, who were ordained by bishops, and so on, going back to the eleven apostles (thus our Church is one, holy, catholic, and apostolic).
So then you are no longer strangers and sojourners, but you are fellow citizens with the holy ones and members of the household of God, built upon the foundation of the apostles and prophets, with Christ Jesus himself as the capstone [also translated keystone]. (19-20)
So Jesus is the key(stone) of the Church that He entrusted to Peter (and his successors) to lead faithfully with the assurance of the guidance of the Holy Spirit. But, beyond that, He also remains truly present, through the action of the priest, to sustain us and give us an unparalleled source of grace, the key to eternal life.