A lot of connections between the words here are lost in translation. The forms of the words here are telling us something important about the universe and the laws of nature, but that is all lost in sloppy, dogmatic translation. Though this is addressed to Peter individually (and this is important because he is a fisherman), it doesn't seem to bestow any special powers on him as much as to describe the nature of knowing and doing things, how to connect and disconnect them. Remember, the context here was Peter realizing who Jesus was and Jesus saying that he couldn't have gotten that idea from other people. A common word that Jesus uses for "understanding" is a Greek word the means "putting things together" and that is important here.

We have to go through this verse carefully to identify what it really says and some of the issues are very technical regarding the difference between Greek words and English ones. I seldom go into this much detail on a verse, but this one seems very important and easy to confuse.

The misunderstand here starts with the term "keys." Jesus lived in a time before keys and lock were in common use. The term Matthew used is more general, meaning any binding used for keeping something closed, from a tie string to a door bar. If we think of it as a "binding" the terms meaning "bind/tie"  and "loosen/untie" fall into sense.  The context is knowledge and the connections between things. Since Peter is a fisherman, this is best seen in the context of tying and untying knots. Knowing how to tied and untie is a matter of life and death for a sailor. It is vital knowledge about how the world works. Tying things together and taking things apart are two ways of knowing reality: the big picture and the separate parts, how things interact, and their individual nature.

The second major misunderstanding comes from the omission of a "when" clause that starts the initial statements about tying and untying on earth.  The first uses of these verbs are in conditional clauses beginning with a Greek word that works like our "when." Those conditional conjunctions are omitted in translation completely, in every version of the Bible. The forms of the Greek "tie" and "untie" verb in those clauses are something that are likely to happen at some time, which is always the case in a conditional clause.

This brings us to the third major problem, the translation of those two verbs as though they were passive, which they could be, and in the future tense, which they are not, in the "in heaven" clauses. These "heaven" clauses are translated as "will be bound/tied" and "will be loosed/untied." However, the active verb here is the "to be," which is in the future tense, but it should be translated as "will exist." The Greek verb "to be" does not act as a "helper" verb as it does in English. It does not make the following verb form, the "tie/untie" participle, passive. Their participle forms could be passive or the middle voice where the subject acts on/by/for themselves but that comes from the verb form, not the preceding verb that is in the middle form, so it "will exist for/by itself."

Next, we have the issue of tenses. The tenses of the second "tie/untie" verbs in the "in heaven" clauses are the past perfect, an action completed in the past. So, this tying/untying in heaven happens before the potential tying/untying by individuals on earth.  The correct way to translate these verbs is either "having been tied/untied in heaven" or "having tied/untied itself in heaven," since the form can be either passive or middle voice. So Peter is doing anything that affects anything in heaven. It already happened there, and it happened by itself before Peter, or any of us, might act on earth.

Finally, the modifying phrase "on the earth" can belong either to the "when you tie it" clause or to the "it will exit" clause. It is ambiguous, probably intentionally so, knowing how Jesus like to play with words. More likely, it ties the two phrases together logically, what we do determine what exists on earth. We can tie or untie, put things together or take them apart, to bring things into existence. That is how it works here on earth. We work by tying some knots, like building a house, and by untying other knots, such as refining metal from rock.

However, what is possible on earth is determined by what has already happened "in the skies," that is in the universe, what the Divine has made possible. We cannot put together what does not go together or take apart what does not come apart. More below on the section about symbolic meaning if you can take anymore.