The Keys are often used as a symbolic reference in the scriptures. Joseph often talked about keys of knowledge and we often hear about priesthood keys.
There are different keys, for different symbolic locks.
A key of knowledge is some bit of information that unlocks or reveals a mystery or locked, inaccessible or un-understandable information. Without the key of knowledge on a particular concept, then answer to the question remains unattainable and the mystery remains locked. I can give you a key of knowledge and never take it back again. Once given it always remains yours.
A priesthood key is authority that accesses a certain priesthood function that without the key we would not have access to. The church uses the term “Priesthood Keys” to explain that certain people in positions hold decision making power or even the ability to do functions or ordinances that those without the keys cannot do. Just as we don’t give all the members of the church keys to the building, the church doesn’t give all members keys or permissions to take certain actions, perform ordinances or make certain decisions. Those things become locked away from others who do not have the keys.
Nothing magical about it.
God does not hold the keys of the church of Jesus Christ of Latter-day Saints. If God wanted to speak in general conference or perform an baptism that was considered valid in the eyes of the Church, God would have to petition whomever had the keys in the church, just as you or I would. However, God holds ALL of the spiritual Keys of the kingdom. He has not given those out to any man or position int the church. This is why D&C 132:7-14 says that any ordinance, promise, covenant, etc. that is made must be ratified by the Holy Spirit of Promise to be valid after the resurrection. It also means that God does not have to work through the LDS Church or it’s leadership to perform any spiritual ordinance or work. He can make covenants and promises without the church that are spiritually binding. Because He holds all the spiritual keys, He can authorize anyone to do anything at any time via the Holy Ghost which tells us all things that we should do. If the Holy Ghost tells you to do something, then you are authorized by God to do it and have been given the keys to do so. We only hold and maintain those keys as long as the spirit is with us, instructing us to use them. When the spirit withdraws or stops telling us to use the keys, they have been taken back and returned to God.
The concept of keys is a perfect way to symbolize something we can’t access directly without some other seemingly unrelated thing.
I can perform a baptism, but without the key of the ratification of the Holy Spirit of promise, the ordinance is spiritually dead and useless. The blessings are inaccessible and remain locked away.
I can perform a baptism that is witnessed and ratified by the spirit, but if I don’t have the key of the Bishop’s authorization, the church refuses to accept that baptism as valid and will not record it on the records of the church. It will still be valid to God and in heaven and after the resurrection, but until you perform it with the key of the Church recognized priesthood, they won’t accept it as valid and it will need to be redone with that key before they unlock the blessings of church membership to a person.