Keys, plural, represent authority of/over something.
If one, say, is a jailer with authority over a jail, they have keys–they have the authority to open and close the doors of the jail. Keys, plural, because the symbolism is one of having the authority to open/close doors. In Revelation 1:18 Jesus says He died, but is alive forever, He has “the keys of Hades and of death” meaning He has overcome death and hell, He is the One with victory and authority–death and hell has no power over Him, He has power over them.
Likewise when Jesus says He gives to Peter (not exclusively to Peter, as He echoes the same thing He said to Peter to the other Apostles in Matthew 18:18, and also in John 20:21-23) the Keys of the kingdom, to bind/loose (open/close) it is about Christ as the One with authority, and by giving those Keys He is giving that authority to His Church (via Peter/the Apostles).
Keys symbolically represent authority. Jesus as the King, means His is the kingdom–i.e. the royal power and authority as King–and to give the keys of the kingdom is to share His Kingly-authority with the one(s) He shares it with. I.e. His Church. It is, of course, within a specific context here: the authority to declare forgiveness “whoever’s sins you forgive are forgiven them” and retain “whoever’s sins you retain are retained”. I can’t go around saying “I forgive you” or “I don’t forgive you” as though I have this authority (I don’t) but through the Apostles it is vested to the Church, and the Church historically therefore has designated certain people as ministers–servants–to exercise the Keys; that is why pastors historically are vested by the Church to preach, to teach, to administer the Sacraments (not in a sacerdotal way, but vocationally and ministerially). In order that, for the good order of Christian life and community, responsible men are trusted with these things (it’s why we see in St. Paul’s letters to Timothy and Titus rigorous criteria about who is to be vetted as a pastor–bishop, presbyter, deacon, etc) Pastors, in this way, are continuing in the apostolic ministry, by holding firm to the apostolic teaching, passing on that teaching through preaching, comforting the Faithful with the Good News of Jesus and calling the Faithful to obedience godly lives and repentance by preaching God’s Commandments, by proclaiming the word (we should remember that for most of Christian history there was no such thing as mass-produced books, and most people were illiterate, and so the ordinary way the majority of Christians encountered and experienced the Bible was when Scripture was read out loud at Christian worship). So pastors were expected to be shepherds, councilors, preachers, teachers, and defenders of the faith for those entrusted to their spiritual care–very much an apostolic work especially after the time the apostles had died and passed on the torch to the next generation–to the pastors of the churches.