The Allegory of the Olive Tree is found in: The Book of Mormon, in the Book of Jacob; the introduction is in the end of Chapter 4 (verses 15-18, though the whole chapter gives you an idea of what was on his (Jacob's) mind when he got on to the topic), the allegory itself comprises Chapter 5, and Jacob's discussion of it is in Chapter 6.
I am going to start out with a little bit of Plato here. I do realize that some of us have been warned explicitly and directly about how we should not allow the philosophies of men to be mingled with scripture; however, the particular idea I am about to use is, in my opinion, sort of floating about in the intellectual ether, anyways; and since Plato's formulation of it is the most famous, I felt that in the interest of letting you know "influences," I would admit that it had come from Plato.
The idea is just this: that there is a realm, somehow, of ideal forms; that on this earth we find All Things Corruptible, but somehow, in that entirely theoretical world of forms, everything is perfect. I'm not going to get sidetracked in to how this turned in to some truly wicked ideas about how physical bodies are inherently evil; suffice it to say that that is a particularly vicious philosophy-scripture combination, which I hate to the depths of my soul.
MOVING on... I have often wondered what the roots and the branches in that allegory were. Clearly the branches have something to do with people; people of the House of Israel, people who aren't, people who get physically moved around the vineyard/earth to suit the purposes of the master.
But the roots, what could they be? I have often wondered. It couldn't just be STRAIGHT the gospel, because then why would there be a danger of the roots being too strong for the branches? It just seemed weird that the gospel could be considered too strong.
However, on a recent run-through I came up with a side-interpretation that I liked a lot. It doesn't have a whole lot to do with moving entire branches of the House of Israel around from one place to another; it does, however, have a lot to do with how I live my life.
If I have something I want to do well, I can't hold myself up to some arbitrary standard of absolute perfection at the beginning of my labors. (Yes, the arbitrary standard of perfection would be one of those Platonic ideal form thingies.) The reason for this is because the standard would be too strong, and I would never feel like working again, because my work would be too weak in comparison and I would just give up. This, in a sense, is like roots being too strong for branches.
If, however, I try to put forth a lot of work (like fruit), comparing it to the standards that I have at the time, then my ability to meet the standards I have will also improve. In photography, for instance, I can take all two hundred or so pictures that my digital camera's memory card will hold; I pick out the best ones; and I delete the rest. As I do this over and over again, the percentage of photographs that meet those standards will gradually grow larger and larger, because my brain will have figured out what kind of things work in order to get those kind of results.
If I want to improve, I will also need better and better standards to meet. I may, for instance, take a class or discuss my work (and others') with other people. Actually doing work-- taking photographs, for instance-- will improve my chances of actually understanding the stuff I am learning in a class or discussing with others. My taste will gradually evolve under these conditions.
Now let's discuss what happens if I don't work. I do realize that the following statement may be controversial in some circles, but I'm making it anyway: no artist works without a purpose, and that purpose drives that artist's standards. For instance, some artists' goal is to shock people (and boy do they seem to do a good job of it sometimes); and I believe that to the extent that this goal drives their work, it drives their artistic standards. If I were to work without any goals, and therefore standards, then my work would be like a dry branch; it would quickly dry up because there would be no framework from which to create. There would be no point, and no sense of direction.
Maybe this really can be applied to living the gospel. Ever since its restoration in Joseph Smith's time, it was revealed a little at a time. They didn't have all of these commandments about living the word of wisdom and going to the temple and doing their family history and doing Family Home Evening on the 6th of April, 1830, because they weren't ready for them. They were ready for: have faith, be baptized, repent, get and follow the Holy Ghost, and endure to the end, including taking the sacrament and following the prophet. The people who did those things became strong in them, and their children didn't have to spend all of their spiritual energy on learning how to do them. Instead, the children spent their energies on the things which are required in their generation. Importantly, people who join the church in that next generation (and there are frequently a lot of them, enough to outnumber the "old-timers") get to draw on the strength of the past generations, as well. In other words, both those who are newly-grafted and those who started out in the gospel gain strength to live up to its ideals because of the efforts of past generations. The gospel really can be too strong, not because it is bad in any way but just because we are weak. Also, the more work we do, the better we understand the best standard to live by; maybe that's what it means in Section 59 about being "blessed with commandments not a few" (verse 4).
Hope that made sense.