Jesus asked His disciples who He was.  Peter correctly answered and then Jesus told Peter “I will give you the keys of the kingdom of heaven”.  What are these keys?

Mat 16:15  He said to them, “But who do you say that I am?”
Mat 16:16  Simon Peter answered and said, “You are the Christ, the Son of the living God.”
Mat 16:17  Jesus answered and said to him, “Blessed are you, Simon Bar-Jonah, for flesh and blood has not revealed this to you, but My Father who is in heaven.
Mat 16:18  And I also say to you that you are Peter, and on this rock I will build My church, and the gates of Hades shall not prevail against it.
Mat 16:19  And I will give you the keys of the kingdom of heaven, and whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven.”

In order to answer what are the keys of the kingdom of heaven we need to know how the Bible use the term “key”.  Let’s take a look at some passages where the word “key” is used.

In Rev 9:1-2 a key was given to the fifth angel which enabled him to open the bottomless pit.

Rev 9:1  Then the fifth angel sounded: And I saw a star fallen from heaven to the earth. To him was given the key to the bottomless pit.
Rev 9:2  And he opened the bottomless pit, and smoke arose out of the pit like the smoke of a great furnace. So the sun and the air were darkened because of the smoke of the pit.

In Rev 20:1-3 a similar situation is described.  An angel had the key to the bottomless pit which enabled him to cast Satan into it and shut him up.

Rev 20:1  Then I saw an angel coming down from heaven, having the key to the bottomless pit and a great chain in his hand.
Rev 20:2  He laid hold of the dragon, that serpent of old, who is the Devil and Satan, and bound him for a thousand years;
Rev 20:3  and he cast him into the bottomless pit, and shut him up, and set a seal on him, so that he should deceive the nations no more till the thousand years were finished. But after these things he must be released for a little while.

In Rev 1:18, Jesus is described as having the keys of Hades (the grave) and of Death, which means Jesus has the power to open the graves and resurrect people to life.

Rev 1:18  I am He who lives, and was dead, and behold, I am alive forevermore. Amen. And I have the keys of Hades and of Death.

From these examples, it is clear that a “key” gives access or power.  The keys of the Kingdom of Heaven allow the possessor access to the Kingdom of Heaven—eternal life.  From Rev 1:18 we know it is Jesus who has power to give people eternal life.  Clearly Peter wasn’t given power to give people eternal life.  However, we know from Scripture that Peter and the other apostles were given knowledge of how to enter the Kingdom of Heaven.  The apostles were given access to the Kingdom of Heaven, to eternal life.  After the crucifixion of Jesus, when the crowds asked Peter they should do, Peter could answer.

Act 2:37  Now when they heard this, they were cut to the heart, and said to Peter and the rest of the apostles, “Men and brethren, what shall we do?”
Act 2:38  Then Peter said to them, “Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit.

The keys of the Kingdom of Heaven are access to the Kingdom of Heaven; they are the knowledge of how to attain the gift of eternal life.