I have decided that I am going to start going over the quotations I can find on keys and see whether I can make head or tail of them.
Given that we really don't have a meaningful sense of keys, and that this is something I have wondered about on and off over many years and still don't have a proper answer, I think it is going to take a careful investigation in the hopes that, by doing so, the matter may be made plain.
Scriptures concerning keys
D&C 6:25 And, behold, I grant unto you a gift, if you desire of me, to translate, even as my servant Joseph.
26 Verily, verily, I say unto you, that there are records which contain much of my gospel, which have been kept back because of the wickedness of the people;
27 And now I command you, that if you have good desires—a desire to lay up treasures for yourself in heaven—then shall you assist in bringing to light, with your gift, those parts of my scriptures which have been hidden because of iniquity.
28 And now, behold, I give unto you, and also unto my servant Joseph, the keys of this gift, which shall bring to light this ministry; and in the mouth of two or three witnesses shall every word be established.
D&C 6 speaks for a time about a gift that had been given. However, this part refers to a different gift as it offers a new gift to Oliver, specifically the gift to translate. It is hard to tell what keys are referred to. We learn elsewhere, of the Urim and Thummim that it requires a key word to operate, and possibly that key word is the "keys of this gift" referred to here.
D&C 130:11 And a white stone is given to each of those who come into the celestial kingdom, whereon is a new name written, which no man knoweth save he that receiveth it. The new name is the key word.
D&C 7:5-8 I say unto thee, Peter, this was a good desire; but my beloved has desired that he might do more, or a greater work yet among men than what he has before done.
6 Yea, he has undertaken a greater work; therefore I will make him as flaming fire and a ministering angel; he shall minister for those who shall be heirs of salvation who dwell on the earth.
7 And I will make thee to minister for him and for thy brother James; and unto you three I will give this power and the keys of this ministry until I come.
8 Verily I say unto you, ye shall both have according to your desires, for ye both joy in that which ye have desired.
D&C 13 Upon you my fellow servants, in the name of Messiah I confer the Priesthood of Aaron, which holds the keys of the ministering of angels, and of the gospel of repentance, and of baptism by immersion for the remission of sins; and this shall never be taken again from the earth, until the sons of Levi do offer again an offering unto the Lord in righteousness.
The keys of the ministering of angels referred to here are only passed on in the Holy Temple. They are given by the power and authority of the Aaronic priesthood to both men and to women. They are not keys to preside or keys of priesthood authority. A person doesn't even need the Aaronic priesthood to receive them, as they are distributed to both men and women. They are keys like those in D&C 129 which allow a man (or woman) to determine whether a ministration is from God.
They are not keys that allow us to command angels to come when we want or to do what we want. When you get the Aaronic priesthood, you do not have the right to command angels any more than you have the right to command God the Holy Ghost when you get the gift of the Holy Ghost. We can no more call angels down from heaven than we can call the Holy Ghost down from heaven. For the lesser is subject to the greater, and God made man a little lower than the angels. In fact, angels will not be subject to us until we reach that point described in described in D&C 132:20 "...Then shall they be gods, because they have all power, and the angels are subject unto them". We may request of the Father, that he may send the Holy Ghost upon us, or that he may send angels to us. But no, we have no more right to call down or command angels than we have a right to command the spirits of our ancestors who presided over the fathers that presided over us.
The Aaronic priesthood also holds the keys of the gospel of repentance, and of baptism by immersion for the remission of sins. Without further explanation here, I assume these are keys to direct that work by revelation, though it may actually reference the fact that the Aaronic priesthood holds the authority to perform the sacrament (an essential part of the gospel of repentance) and to perform baptism.