Perhaps the easiest example of this is Christ, himself. When He stood before His Pharisaical accusers, He spoke not one word to defend Himself. Can you imagine what it is like, to stand silent while others rage and taunt you, knowing that your silence will lead to your death?
Because this is a divine attribute I am in dire need of developing, I don't understand it completely. One thing is becoming clear to me, that the most common time to be silent is in the face of willful ignorance. There is no point in speaking, then. Once testimony has been borne, there is nothing more to say to those who are so embroiled in their own illusion of reality, they will afford no room for another opinion.
My time spent on LDS blogs has helped me learn this balancing trait. When I first began commenting, I often thought that people presented problems online because they wanted a solution. I naively assumed that they were looking to change themselves, to understand a little more of the Gospel of Christ. I still think that many seek understanding, but there are mostly times and places online where the true goal is to find camaraderie, not solutions. At times like this, it is sometimes better to be silent.
There have also been times when I have heard silence from the Lord in answer to my pleas to Him for understanding. It is at these times when I have had to accept His silence before I could feel His presence at my side. I have come to realize that sometimes I am not ready for an answer, and that an answer would sometimes harm me more than it would help me. I find this also true with my own daughter, at times. There are just some things she has to work out on her own, and all I can do is sit beside her silently.
To take this one step further, I have found that occasionally in scripture, the Lord grants a person the ability to bind or seal in earth and in heaven. Often, this is connected to the Priesthood power, but it seems to be more than the Priesthood as we commonly understand it. The best recounting of this, and one of my favorite scriptures, is the moment the Lord declares His utter trust in Nephi, son of Helaman. The Lord says to him:
"Blessed art thou, Nephi, for those things which thou hast done; for I have beheld how thou hast with unwearyingness declared the word, which I have given unto thee, unto this people. And thou hast not feared them, and hast not sought thine own life, but hast sought my will, and to keep my commandments. And now, because thou hast done this with such unwearyingness, behold, I will bless thee forever; and I will make thee mighty in word and in deed, in faith and in works; yea, even that all things shall be done unto thee according to thy word, for thou shalt not ask that which is contrary to my will. Behold, thou art Nephi, and I am God. Behold, I declare it unto thee in the presence of mine angels, that ye shall have power over this people, and shall smite the earth with famine, and with pestilence, and destruction, according to the wickedness of this people.What I would not give for such a declaration of faith! This is God Himself telling Nephi that He trusts him!
Helaman 10:4-5, emphasis added
And how did he obtain that trust? By seeking the will of God, by putting Him first without wearying. (And oh, how I weary!) He declared what the Lord wanted him to declare, no less . . . and no more. He knew NOT to ask as much as he knew to ask. Sometimes I wonder if the Lord could trust him because he knew when to speak and when to keep silent.