The breakdown of his talk is very simple. There are two lines of communication between us and God. One is through personal revelation, while the other is through priesthood authority. Both are essential for receiving revelation from God and neither one can function without the other.
In regards to personal revelation Elder Oaks stated,
"This personal line of communication with our Heavenly Father through His Holy Spirit is the source of our testimony of truth, of our knowledge, and of our personal guidance from a loving Heavenly Father. It is an essential feature of His marvelous gospel plan, which allows each one of His children to receive a personal witness of its truth."If we are to learn the doctrine of salvation it is not sufficient to listen to and to memorize or accept blindly the teachings of those in authority in the Church, because the personal line of communication is the source of our testimony of truth and of our knowledge of eternal doctrine. But lest we think that this is an unrestrained endorsement of the "priesthood of all believers" he cautions us that, "in its fulness the personal line does not function independent of the priesthood line." and that, "we cannot communicate reliably through the direct, personal line if we are disobedient to or out of harmony with the priesthood line."
So while it is necessary for each individual to discover for themselves the truth and to learn the doctrine through the direct, personal line of communication from God, this line of communication does not function properly if we are separated from the priesthood line of communication.
Elder Oaks explains that unlike the personal line which has no "mortal mediator" the priesthood line, "has the additional and necessary intermediaries of our Savior, Jesus Christ; His Church; and His appointed leaders." This means that in order for the priesthood line to function there must be "mediators" through which the revelation is communicated. This means that no one can function independently in the priesthood line because the purpose of the priesthood line is to organize the Church and to allow the ordinances to be performed. As he put it,
"The priesthood line is the channel by which God has spoken to His children through the scriptures in times past. And it is this line through which He currently speaks through the teachings and counsel of living prophets and apostles and other inspired leaders. This is the way we receive the required ordinances. This is the way we receive calls to service in His Church. His Church is the way and His priesthood is the power through which we are privileged to participate in those cooperative activities that are essential to accomplishing the Lord’s work. These include preaching the gospel, building temples and chapels, and helping the poor."So while we may learn and understand the doctrine through the personal line of communication, it is through the priesthood line that we first receive the doctrine. The priesthood line is also necessary for the performance of ordinances as they are things that, by definition, we cannot perform on ourselves.
One of the potential problems that Elder Oaks pointed out was that there are those who think that they can rely solely on the personal line of communication and disregard the priesthood line.
"Some members or former members of our church fail to recognize the importance of the priesthood line. They underestimate the importance of the Church and its leaders and its programs. Relying entirely on the personal line, they go their own way, purporting to define doctrine and to direct competing organizations contrary to the teachings of prophet-leaders."This way of thinking leads these people to criticize the leaders of the Church because in their view the Church leaders "just don't get it", or to say things like "the leadership has no special claim to inspiration or revelation" which is another way of saying, "I don't need the influence of priesthood authority". The end result is to separate the individual from the priesthood line of communication where spiritually they will wither and die (as Jesus put it, "As the branch cannot bear fruit of itself, except it abide in the vine; no more can ye, except ye abide in me." (see John 15:4-6)).
This way of thinking also leads individuals to assert that, "the church has gone off course and is not on the track it was meant to be." In saying this they fail to recognize that God uses the Church and the priesthood in the Church to direct its course. So to assert that the Church as a whole, or even just the Church leaders as a whole, have gone astray is to assert that God is not directing His Church and that the priesthood line of communication has become corrupted, all the while not questioning the clarity of their personal line of communication. This does not mean that all things that come from Church leaders are perfect and infallible, but because the priesthood line of communication is the method through which God disseminates his word, then it is in His best interest (i.e. our interest) to keep those channels free and clear of corruption. But as a check we have the personal line of communication. Thus we whole heartedly reject the notion of blind faith. Blindly accepting the direction and teachings of our leaders is to forget the personal line of communication which goes contrary to the very teachings being given by our priesthood leaders.
As Elder Oaks put it,
"We must use both the personal line and the priesthood line in proper balance to achieve the growth that is the purpose of mortal life. If personal religious practice relies too much on the personal line, individualism erases the importance of divine authority. If personal religious practice relies too much on the priesthood line, individual growth suffers. The children of God need both lines to achieve their eternal destiny. The restored gospel teaches both, and the restored Church provides both."