A tame olive tree is one that is cultivated by the master of the vineyard, specifically grown to produce good olives. The olive tree is a carefully chosen simile for several reasons:
"For centuries the olive branch has been associated with peace. When the dove returned to Noah in the ark, it carried in its beak an olive leaf, as though to symbolize that the earth was again at peace with God. (See Genesis 8:11) The olive branch was used in both Greece and Rome to signify peace, and it is still used in that sense in the great seal of the United States where the American eagle is shown grasping an olive branch in his talons…
"There is further symbolic significance in that the olive tree is different from most other fruit-bearing trees in the manner of its beginning. If the green slip of an olive tree is merely planted and allowed to grow, it develops into the wild olive, a bush that grows without control into a tangle of limbs and branches that produce only a small, worthless fruit. (See Harold N. and Alma L. Moldenke, Plants of the Bible, p. 159) To become the productive ‘tame’ olive tree, the main stem of the wild tree must be cut back completely and then a branch from a tame olive tree must be grafted into the stem of the wild one. With careful pruning and cultivating the tree will begin to produce its first fruit in about seven years, but it will not become fully productive for nearly fifteen years. In other words, the olive tree cannot become productive in and of itself; it requires grafting by the husbandman to bring it into production. One remembers the figure used by Jesus to describe himself, his Father, and those that serve them: ’I am the true vine, and my father is the husbandman. Every branch in me that beareth not fruit he taketh away: and every branch that beareth fruit, he purgeth it, that it may bring forth more fruit. Now ye are clean through the word which I have spoken unto you. ’ (John 15:1-3) The word purgeth in Greek means ’pruned,’ and in Greek verse 3 keeps the metaphor and says, ’ Now ye are pruned.’ God is the husbandman and prunes off the wild branches of our spiritual lives if we will but submit to his tender care. Thus we become like the tame olive tree…
"’The wild olive is a kind of reversion to the primitive plant—such as occurs also with the fig and almond—and it takes place whenever the growth of the olive is neglected….
“‘In most neglected olive groves numerous little bushes of the ’wild olive’ may be seen, which, though very unlike the cultivated tree—having a shorter, smaller, and greener leaf and a stiffer, more prickly stem—are nevertheless derived from it. As a rule the wild olive is but a shrub, but it may grow into a tree and have small but useless ’berries.’ Where groves of wild olives are found in Palestine, they are probably always the descendants of cultivated trees long ago destroyed,’ (James Hastings, ed., Dictionary of the Bible, s.v. ”Olive.")
“The olive tree is remarkable for two other characteristics that are quite unlike other fruit-bearing trees. First, though requiring nearly fifteen years to come into full production, it may produce fruit for centuries. Some trees now growing in the Holy Land have been producing abundantly for at least four hundred years. The second amazing quality of the tree is that as it finally does grow old and begin to die, the roots send up a number of new green shoots which, if grafted and pruned in regular fashion, will mature to full-grown olive trees again. Thus, while the tree itself may produce fruit for centuries, the root of the tree may go on producing fruit and new trees for millennia. It is believed that some of the ancient olive trees in Israel today come from trees that were [in existence] when Christ was alive on the earth.” (Book of Mormon Student Manual, 1981, pp. 138-9)