Zionism is the ideological position of furthering and supporting the formation and continuation of a Jewish State in Israel. It was founded and advanced chiefly by secular movements and leaders (most prominently the atheist Theodor Herzl), as an answer to the problem of Anti-Semitism. The idea was that anti-Semitism is unavoidable in any country where Jews are a minority, so the Jews should establish a country where they are the rulers and the absolute majority. In this way anti-Semitism would not be able to raise its head. That this state should be in the land of Israel was not initially a requirement of Zionism, but later historical longings for their ancestral land and the realization that only this land will have the strong-enough appeal to draw the many Jews required convinced the Zionists that Israel was the only possible state where Zionism can be implemented.
The appeal of Zionism grew strong due to the increase in anti-Semitism in the 20th century. First the rise of anti-Semitism in Russia forced many to escape it. Then WWII and the ensuing Holocaust resulted in a flood of refugees from all over Nazi-controlled and Nazi-allied Europe and beyond. Then, following the formation of the state of Israel, a great increase in Muslim anti-Semitism led to the expulsion and exile of over 700,000 Jews from the Arab world. Further immigration continued over the years, including most prominently over a million immigrants from the former Soviet Union following its collapse, who immigrated from a combination of escaping anti-Semitism, idealism, and economic incentives.
As a largely secular enterprise, Zionism had been and still is rejected by a large part of the ultra-Orthodox (Hasidi and Haredi) Orthodox Jews, who consider it against blasphemous. It has, nevertheless, managed to gain the support of several rabbis, most prominently rabbi Abraham Isaac Kook that founded religious Zionism and much of Modern Orthodoxy. Kook connected Zionism to Messianism and a view of the state of Israel as itself holy and an instrument of salvation. This ideology was greatly strengthened by Israel's military success and conquests. As a result, religious Zionists claim all of the land of Israel (including especially the mountainous regions, the West Bank) as the holy land granted to them by God and see its conquest, settlement, and ultimately the establishment of a wholly-Jewish society there as their divine mission in life. This Religious Judaism drives much of the conflict with the Palestinians. Most Israeli settlers belong to this idealogical-religious stream, as do most racist groups and activities, including the few Jewish terrorists (including, most prominently, Yigal Amir that assassinated the Iaraeli prime-minister to prevent peace, and Baruch Goldstein that conducted a ghastly massacre at the Cave of the Patriarchs in the city of Hebron) and the conductors of numerous acts of oppression and "reprisal" by settlers against the Palestinians.
Most Zionist Jews reject these views, seeing Israel instead as their ancestral homeland to which they have the right to return and as a modern democratic state that has a right to continue to exist.
From its beginning Zionism has been argued against by Jews on the grounds that it will increase anti-Semitism. This has been borne out by the expulsion of Jews from Arab countries, and the increased animosity towards Jews in the Muslim world following the assumption of Jewish control over the holy land. Israeli policies also frequently lead to increases in anti-Semitism when local Jews in exile (who have nothing to do with them) suffer reprisals, and the lives of many Israelis themselves are frequently threatened by war or terror. On the other hand, the Zionist movement has also been vindicated in that Israel is nonetheless perceived as a place safe from anti-Semitic persecution where Jews can come to live safely and freely, and in the great revival of Hebrew culture and the self-governance of Jews that it allowed.
Zionism has an in-built tension in it in that it calls for the establishment of a liberal democracy on the one hand but for a Jewish state on the other. Modern Zionism deals with this tension by allowing and encouraging only Jewish immigration into Israel, but fostering equality and democracy within, extending full rights to non-Jews as well as Jews. The tension is nevertheless powerful, and manifests in two ways. First, in practice Palestinians of Israeli citizenry are often discriminated against and, especially amongst the religious Jews, are often considered to have no right to a say on issues of national security or even, too often, no right to vote at all. Secondly, while Israel has conquered extensive parts with native Arab and Palestinian populations, including the West Bank and Golan Heights, it has not annexed them or extended full citizenship to the residents, nor allowed a right of return to the refugees of these wars. Instead, it has encouraged the development of Israeli-Jewish settlements, and addressed the local inhabitants in various ways according to the local conditions, with the overall strategy of ensuring the safety and freedom of its Israeli (Jewish) population and settlements while maintaining control (as much as possible) over the lands.
It is becoming increasingly obvious to Israel and the international community that this is not a tenable long-term solution, and the Jewish State is now at a crossroads. The favored international solutions seems to be the "two states" solution, where Israel is split into two states, one for Jews (with a Palestinian minority) and one for Palestinians (with virtually no Jews). In this way the Jews can still have a democratic Jewish state free of antisemitism but the Palestinians can have their own self-determination on their own ancestral land as well. However, this solution does not satisfy the religious Zionists that seek to control especially the mountain regions that the Palestinians inhabit, nor the many Palestinian in the diaspora that seek to return to their specific homes and not to a nebolous Palestinian Authority. The preferred Israeli solution appears to be a Palestinian Autonomy, where Israel would in effect become an "empire" with colonies in the West Bank and, possibly, Gaza, that would otherwise be self-governing regions under local governments without military power. Naturally, this solution is strongly opposed by the Palestinians in the conquered territories themselves, who want sovereignty, but many Israelis feel no other solution could guarantee their own safety and are unwilling to let go of the settlements and the historically-significant mountains. Meanwhile, increasingly on both sides advocates from the Left argue that a division is not geographically and geo-politically possible, and that the only solution is a single unified democratic state. Such a state would, however, spell the end of Zionism as Jews would no longer form an overwhelming majority in it, and most Israelis don't trust the Palestinians to adhere to democratic values, and fear for their safety and property in such a union - while most Palestinians don't want to share "their" country with the immigrant Jews, and fear that their great wealth and power would mean they would effectively rule the country even from a minority position. And in the meantime, Israel's military enemies such as Iran and its supportive Hezbullah of Lebanon or the Hamas movement in Gaza prophecy the collapse of the Zionist Regime and periodically instigate attempts to militarily harass - and, ultimately, conquer - parts of it. In whichever way history goes, the future of the Jewish State, the end of all Zionist movements, should be... interesting.