I had heard or read of that passage ages ago. I see from Earnest’s post above, that Rutherford (as usual) came up with a pile of pseudo-mystical nonsense, in interpreting it.
An interpretation in “Christendom” would likely be along the following lines. The first and most obvious point is to look at the context. Someone called Jotham gave a speech that included the tree allegory. It is clear in context that Jotham was not reporting an event; he was just being allegorical. Further, Jotham was speaking in order to persuade a crowd that Abimelech (who had just made himself king by force and murder) should not be accepted as king. The idea of brambles (a low-lying plant) offering shade is a joke, and brambles being a plant of no virtue, and also flammable (ie dangerous) is part of the allegory.
Thus, the explanation and interpretation of the passage is relatively simple and straightforward; ie don’t choose a morally corrupt person as your ruler. (Also, notice how the least worthy tree/plant is the one to demand to be the ruler, or else.)