What is the meaning of "whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven."?

Before Jesus left His disciples and went to heaven, He gave them some special authority that has confused many people. We see this authority in the following two passages:

Matthew 16:19And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven.
See All... - "And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven."

John 20:23Whose soever sins ye remit, they are remitted unto them; and whose soever sins ye retain, they are retained.
See All... - "Whose soever sins ye remit, they are remitted unto them; and whose soever sins ye retain, they are retained."

These two passages are referring to the same general power. In both cases, something done by the disciples on earth is confirmed in heaven by God. However, there are some differences as well. Matthew 16:19And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven.
See All... deals with binding and loosing things and is given as a power specifically to Peter ("thee" and "thou" are singular pronouns and therefore refer directly to Peter alone). John 20:23Whose soever sins ye remit, they are remitted unto them; and whose soever sins ye retain, they are retained.
See All... deals with sins being remitted (that is, forgiven) or retained and this authority is given to the apostles in general ("ye" is plural and would refer to all the apostles). Because of these differences, we need to look at the verses separately.

In Matthew 16:19And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven.
See All..., Peter is given power over the keys of heaven. This power is demonstrated in the binding or loosing of things on earth that need to be bound or loosed in heaven. Certainly, the other disciples knew that Peter had this authority and had to respect this authority that was given to him. There are two incidents which illustrate this authority in the later ministry of Peter. The first incident is in Acts 1:15-26 [15] And in those days Peter stood up in the midst of the disciples, and said, (the number of names together were about an hundred and twenty,) [16] Men and brethren, this scripture must needs have been fulfilled, which the Holy Ghost by the mouth of David spake before concerning Judas, which was guide to them that took Jesus. [17] For he was numbered with us, and had obtained part of this ministry. [18] Now this man purchased a field with the reward of iniquity; and falling headlong, he burst asunder in the midst, and all his bowels gushed out. [19] And it was known unto all the dwellers at Jerusalem; insomuch as that field is called in their proper tongue, Aceldama, that is to say, The field of blood. [20] For it is written in the book of Psalms, Let his habitation be desolate, and let no man dwell therein: and his bishoprick let another take. [21] Wherefore of these men which have companied with us all the time that the Lord Jesus went in and out among us, [22] Beginning from the baptism of John, unto that same day that he was taken up from us, must one be ordained to be a witness with us of his resurrection. [23] And they appointed two, Joseph called Barsabas, who was surnamed Justus, and Matthias. [24] And they prayed, and said, Thou, Lord, which knowest the hearts of all men, shew whether of these two thou hast chosen, [25] That he may take part of this ministry and apostleship, from which Judas by transgression fell, that he might go to his own place. [26] And they gave forth their lots; and the lot fell upon Matthias; and he was numbered with the eleven apostles.
See All... where Peter stands up in the midst of the disciples and authorizes the choosing of a disciple to replace Judas. He bound Mathias on earth and he was evidently bound in heaven. The second incident is in Acts 10-11 where God uses Peter to open the door of faith to the Gentiles. The door was loosed on earth and in heaven at the same time.

The special apostolic authority referred to in John 20:23Whose soever sins ye remit, they are remitted unto them; and whose soever sins ye retain, they are retained.
See All... concerns the remitting and retaining of sins and is given to the apostles. To remit means to refrain from exacting or requiring payment for a debt. That is, the apostles were given the authority to determine which sins are remitted (that is, forgiven and not paid for immediately) and to determine which sins are retained (that is, held to the person’s account and paid for immediately). Again, there are two examples of this authority in the ministry of Peter. In the case of Ananias (Acts 5:1-5 [1] But a certain man named Ananias, with Sapphira his wife, sold a possession, [2] And kept back part of the price, his wife also being privy to it, and brought a certain part, and laid it at the apostles' feet. [3] But Peter said, Ananias, why hath Satan filled thine heart to lie to the Holy Ghost, and to keep back part of the price of the land? [4] Whiles it remained, was it not thine own? and after it was sold, was it not in thine own power? why hast thou conceived this thing in thine heart? thou hast not lied unto men, but unto God. [5] And Ananias hearing these words fell down, and gave up the ghost: and great fear came on all them that heard these things.
See All...), Peter retained his sins and Ananias and his wife paid for them immediately with their lives. However, in the case of Simon (Acts 8:17-24 [17] Then laid they their hands on them, and they received the Holy Ghost. [18] And when Simon saw that through laying on of the apostles' hands the Holy Ghost was given, he offered them money, [19] Saying, Give me also this power, that on whomsoever I lay hands, he may receive the Holy Ghost. [20] But Peter said unto him, Thy money perish with thee, because thou hast thought that the gift of God may be purchased with money. [21] Thou hast neither part nor lot in this matter: for thy heart is not right in the sight of God. [22] Repent therefore of this thy wickedness, and pray God, if perhaps the thought of thine heart may be forgiven thee. [23] For I perceive that thou art in the gall of bitterness, and in the bond of iniquity. [24] Then answered Simon, and said, Pray ye to the LORD for me, that none of these things which ye have spoken come upon me.
See All...), the sins were remitted and Simon was given another chance to get things straight.

This authority given to the apostles was a special authority. No scriptures indicate that it passed on to anyone else of New Testament times or to anyone of later times. It was part of the authority and power of the apostles to confirm the preaching of a new message to Jews and then to Gentiles as well. In that sense, it worked like the sign gifts of the apostolic age (see Mark 16:17-20 [17] And these signs shall follow them that believe; In my name shall they cast out devils; they shall speak with new tongues; [18] They shall take up serpents; and if they drink any deadly thing, it shall not hurt them; they shall lay hands on the sick, and they shall recover. [19] So then after the Lord had spoken unto them, he was received up into heaven, and sat on the right hand of God. [20] And they went forth, and preached every where, the Lord working with them, and confirming the word with signs following. Amen.
See All...). With the completion of the New Testament and the establishment of a people known as Christians, these sign gifts were no longer part of God's plan for reaching the world. And, since it was not passed on, it has nothing to do with Peter being the first pope as claimed by the Roman Catholics.