Grafting is a horticultural process of uniting two different (but genetically compatible) plants so that they grow as one i.e. surgically inserting a branch, or shoot, of one plant into the tissue of another; after the union heals, they are a single living entity. The purpose of grafting is most often to unite a root stock with grafted parts that together produce some desired result e.g. peach trees tolerate sandy soil better than plum trees; plum grafts are made to peach root stock to permit the better growing of plums in sandy soil. Grafting has been known for thousands of years, and was well-known to the people of Bible History, mostly from olive trees. Some varieties of olive trees had very vigorous roots, but produced poor olives, and vice-versa, so branches from good quality olive trees were grafted onto olive trees of stronger root stock which together made an all-round superior olive tree.
Grafting In The Bible
Grafting was used as an analogy of how, and why, Gentiles can become one with spiritual Israel (see Physical and Spiritual Israel). Paul also explains why many of physical Israel cannot see, because "that blindness in part is happened to Israel." It's why many cannot understand, yet (those of Israel who could, but rejected the Truth, are another matter):
"For I speak to you Gentiles, inasmuch as I am the apostle of the Gentiles, I magnify mine office: If by any means I may provoke to emulation them which are my flesh, and might save some of them. For if the casting away of them be the reconciling of the world, what shall the receiving of them be, but life from the dead? For if the firstfruit be holy, the lump is also holy: and if the root be holy, so are the branches."
"And if some of the branches be broken off, and thou, being a wild olive tree, wert grafted in among them, and with them partakest of the root and fatness of the olive tree; Boast not against the branches. But if thou boast, thou bearest not the root, but the root thee. Thou wilt say then, The branches were broken off, that I might be grafted in. Well; because of unbelief they were broken off, and thou standest by faith. Be not highminded, but fear: For if God spared not the natural branches, take heed lest He also spare not thee."
"Behold therefore the goodness and severity of God: on them which fell, severity; but toward thee, goodness, if thou continue in his goodness: otherwise thou also shalt be cut off. And they also, if they abide not still in unbelief, shall be grafted in: for God is able to graft them in again. For if thou wert cut out of the olive tree which is wild by nature, and wert grafted contrary to nature into a good olive tree: how much more shall these, which be the natural branches, be grafted into their own olive tree?"
"For I would not, brethren, that ye should be ignorant of this mystery, lest ye should be wise in your own conceits; that blindness in part is happened to Israel, until the fulness of the Gentiles be come in. And so all Israel shall be saved: as it is written, There shall come out of Sion [see Who, What or Where Is Zion?] the Deliverer, and shall turn away ungodliness from Jacob" (Romans 11:13-26 KJV)
The "engrafted word" is used an analogy for those who have become Believers in the Word of God:
"Wherefore lay apart all filthiness and superfluity of naughtiness, and receive with meekness the engrafted word, which is able to save your souls. But be ye doers of the word, and not hearers only, deceiving your own selves."
"For if any be a hearer of the word, and not a doer, he is like unto a man beholding his natural face in a glass: For he beholdeth himself, and goeth his way, and straightway forgetteth what manner of man he was. But whoso looketh into the perfect law of liberty, and continueth therein, he being not a forgetful hearer, but a doer of the work [see "Works" Means Obedience], this man shall be blessed in his deed." (James 1:21-25 KJV)
Fact Finder: What did Jesus Christ say about "the vine and the branches"?