The short and simple answer is, The keys to the Kindom of Heaven (malchut shamiem)is the Good News of the Gospel of Yeshua haMashiach (Jesus the Christ). That is it, there is no more to add to it, however, because of the rest of the paragraph more information is required.
Here is a quote that I found on the Internet. I will not give the address because I believe it to be a false teaching and it leads so many New Age Christians to fail! And I'll give unto you the keys of the kingdom of heaven: and whatsoever you bind on earth shall be bound in heaven: and whatsoever you loose on earth shall be loosed in heaven'. Providing, of course, it's bound or loosed by faith. Because God's Word does not return to Him void, but accomplishes that for which it was sent. And if we abide in His Word, and His Word abides in us, we can ask anything in His Name, and He'll BIND or LOOSE it.
Acts 2:38-39 38 Peter replied, "Repent and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of your sins. And you will receive the gift of the Holy Spirit. 39 The promise is for you and your children and for all who are far off-for all whom the Lord our God will call." (from New International Version) *******************************
"And the "key" of the house of David I will lay upon his shoulder; He shall open and no one shall shut, He shall shut and no one shall open." Isaiah 22:22.
"And to the angel (messenger) of the assembly (church in Philadelphia write: These are the words of the Holy One, the True One, He Who has the "key" of David, Who opens and no one shall shut, Who shuts and no one shall open: I know your [record of] works and what you are doing. See! I have set before you a door wide open which no one is able to shut; I know that you have but little power, and yet you have kept My Word and guarded My Message and have not renounced or denied My Name. Take note! I will make those of the synagogue of satan who say they are Jews and are not, but lie - behold, I will make them come and bow down before your feet and learn and acknowledge that I have loved you. Because you have guarded and kept My word of patient endurance [have held fast the lesson of My patience with the expectant endurance that I give you], I also will keep you [safe] from the hour of trial (testing) which is coming on the whole world to try those who dwell upon the earth. I am coming quickly; hold fast what you have, so that no one may rob you and deprive you of your crown. He who overcomes (is victorious), I will make him a pillar in the sanctuary of My God and the name of the city of My God, the new Jerusalem, which descends from My God out of Heaven, and My own new name. He who can hear, let him listen to and heed what the Spirit says to the assemblies (churches)." Revelation 3:7-13.
Strong's Concordance - Key
Isaiah 22:22 (4668) an opener - key (6605) to open wide, to loosen, plough, carve - appear, break forth, draw (out), let go free, ungird, unstop, have vent, loose, be set open, put off.
Matthew 16:19 (2807) Key (as shutting a lock) (2808) to close - shut (up).
The Eerdmans Bible Dictionary - Keys, Power of - The symbol of apostolic authority granted by . A common view in the ancient world was that the earth was separated from the upper and lower worlds by locked doors, access to which was only through the angelic being or deity who held the keys (GK. Kleis). Figuratively, then, keys represent the power and authority to control access to whatever is behind the locked door (e.g., Rev. 9:1; 20:1).
Paul said in I Corinthians 2:4-5, "And my speech and my preaching was not with enticing words of man's wisdom, but in demonstration of the Spirit and of power: That your faith should not stand in the wisdom of men, but in the power of God."
God help us all at this point. II Corinthians 3:6 says, "Who also hath made us able ministers of the new testament; not of the letter, but of the spirit: for the letter killeth, but the spirit giveth life." So we see the Word alone is not sufficient but it must be accompanied by the Spirit and backed by Holy Spirit anointing.
Therefore, we conclude that God's Word and His Spirit are the keys to the kingdom of heaven and open an access into Christ and salvation. Hebrews 5:9 says that Christ "...became the author of eternal salvation unto all them that obey him." So we see that as one obeys God's Word and meets the conditions laid down therein for being saved confession of sin (I John 1:9), repentance (II Corinthians 7:10-11; Acts 3:19; Luke 24:47; Mark 1:14-15), restitution (II Corinthians 7:10; Luke 19:8; Ezekiel 33:15), and faith in the Lord Jesus Christ and the merits of His shed blood, the door swings wide open to him and he is accepted into the kingdom of God.
This is exactly what Jesus gave to Peter in this text and also to all the apostles, and further to their successors throughout this gospel age of time; even NOW to the holy, God-called, God-qualified, Holy Spirit filled ministry which God has in the Church and in the world at this present time. They also possess these keys to the kingdom of heaven.
In Matthew 28:19-20, Jesus said to His disciples, "Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you alway, even unto the end of the world." It is evident here that Jesus ordained and commissioned a perpetual ministry who would have the same power and authority (the same keys of the kingdom God's Word and Spirit) as those early ones had. This was to last unto the end of the world and just as God encouraged Joshua by telling him, "...As I was with Moses, so I will be with thee," (Joshua 3:7) he says the same to His true ministers today, "As I was with Peter, James and John and their immediate brethren, so am I with you." His promise was, "...I am with you alway, even unto the end of the world." (Matthew 28:20.) That reaches to us down here in this end of the gospel age the same as it applied to those disciples in the early beginning of this gospel age.