Why is Israel important in Bible prophecy?
Israel stands at the center of Bible prophecy because it is the chosen nation through whom God's covenant promises, the Church, and end time events all unfold, and its future national salvation and restoration is guaranteed by the Father's unbreakable calling upon them.
Israel is important in Bible prophecy because the Lord made an everlasting covenant with this nation, and it is through Israel that the Church itself was formed. Even though the nation as a whole rejected Jesus as Messiah for a season, that rejection served the purpose of bringing in the Gentiles, and Paul teaches that the gifts and calling of God are without repentance, meaning God does not take back what He has spoken over Israel. Their blindness is only in part, and there is a faithful remnant, saved even now, that keeps the promise alive.
Israel's place in prophecy is tied to a coming day of national conversion. Scripture teaches that all Israel shall be saved, that the Deliverer shall come out of Zion and turn away ungodliness from Jacob, and that at the end of the age the Lord will return and Israel will see Him and receive Him, saying, Blessed is He who comes in the name of the Lord. This is described as happening in one day, when the Lord will remove the iniquity of the land and cast their sins into the depths of the sea, likely just before the Millennium begins, since the Jewish remnant will be the keepers of the Temple and the ones who offer sacrifices during that reign.
Israel is also central to end time events surrounding the Antichrist. The Temple will be rebuilt in Jerusalem, near a Gentile edifice, and this rebuilding itself testifies that Israel has not yet accepted Jesus as Messiah, for they will receive one who comes in his own name after having rejected the One who came in His Father's name. The Antichrist's dealings with Israel, his broken covenant, his craft and destruction, and his opposition to the Prince of princes are all bound up with Israel's story in the last days, and the Jewish remnant will be told to flee to the mountains when he stands in the Temple declaring himself God.
Because of all this, believers are told not to boast against Israel or hold contempt for the Jewish people, since we who believe are grafted into their olive tree by grace, while unbelieving natural branches were broken off. The severity and goodness of God are both on display in this: Israel now walks under God's severity, and we walk under His goodness, but if they do not remain in unbelief they will be grafted back in, for God is able to do this. Our calling is continual prayer for the peace of Jerusalem and preaching the gospel to Israel as a mission field, remembering that in Abraham's seed all families of the earth are blessed.
The scriptures
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 the Deliverer, and shall turn away ungodliness from Jacob: For this is my covenant unto them, when I shall take away their sins. As concerning the gospel, they are enemies for your sakes: but as touching the election, they are beloved for the fathers’ sakes. For the gifts and calling of God are without repentance. For as ye in times past have not believed God, yet have now obtained mercy through their unbelief: Even so have these also now not believed, that through your mercy they also may obtain mercy. For God hath concluded them all in unbelief, that he might have mercy upon all. O the depth of the riches both of the wisdom and knowledge of God! how unsearchable are his judgments, and his ways past finding out!
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 graffed 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 graffed in: for God is able to graff them in again. For if thou wert cut out of the olive tree which is wild by nature, and wert graffed contrary to nature into a good olive tree: how much more shall these, which be the natural branches, be graffed into their own olive tree?
And I will bless them that bless thee, and curse him that curseth thee: and in thee shall all families of the earth be blessed.
Hear now, O Joshua the high priest, thou, and thy fellows that sit before thee: for they are men wondered at: for, behold, I will bring forth my servant the BRANCH. For behold the stone that I have laid before Joshua; upon one stone shall be seven eyes: behold, I will engrave the graving thereof, saith the LORD of hosts, and I will remove the iniquity of that land in one day. In that day, saith the LORD of hosts, shall ye call every man his neighbour under the vine and under the fig tree.
Who is a God like unto thee, that pardoneth iniquity, and passeth by the transgression of the remnant of his heritage? he retaineth not his anger for ever, because he delighteth in mercy. He will turn again, he will have compassion upon us; he will subdue our iniquities; and thou wilt cast all their sins into the depths of the sea.
I am come in my Father’s name, and ye receive me not: if another shall come in his own name, him ye will receive.
And there was given me a reed like unto a rod: and the angel stood, saying, Rise, and measure the temple of God, and the altar, and them that worship therein. But the court which is without the temple leave out, and measure it not; for it is given unto the Gentiles: and the holy city shall they tread under foot forty and two months.
And in the latter time of their kingdom, when the transgressors are come to the full, a king of fierce countenance, and understanding dark sentences, shall stand up. And his power shall be mighty, but not by his own power: and he shall destroy wonderfully, and shall prosper, and practise, and shall destroy the mighty and the holy people. And through his policy also he shall cause craft to prosper in his hand; and he shall magnify himself in his heart, and by peace shall destroy many: he shall also stand up against the Prince of princes; but he shall be broken without hand.
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.