Land owned by Jews prior to 1948 was bought and paid for by the Jews who moved to Palestine, Jewish organizations in Europe set up to fund the Zionist movement, and by wealthy Jews such as Edmond Rothschild, who regularly gave money to zionists in Palestine.

In 1947, UN General Assembly Resolution 181 was passed, which would partition Palestine into an Arab and Jewish state, and left Jerusalem to be under international rule (as u/tayaravaknin points out, this resolution never came to fruition). British forces had been keeping the peace in Palestine, but Britain was now eager to withdraw its forces. On May 14, 1948, the British Mandate over Palestine expired, and that night in Tel Aviv, David ben Gurion declared the existence of the State of Israel. Surrounding Arab states which opposed the UN Resolution attacked Israel but were driven back. During and after what the Israelis call the War of Independence and what Arabs refer to as al-Nakba (the disaster), Arabs in Jewish areas of Palestine fled to neighboring states or Arab zones. Haifa, for example, had a large Arab community prior to 1948, but many left and never returned. Those Arabs that did stay were granted full Israeli citizenship and today even fight in the Israeli Armed forces. Those Arabs that fled, expecting to return to their homes after the Jews were expelled from the land, lost their gamble and their land.

The largest loss of Palestinian land came not to the Jews, however, but to Jordan, one of the countries that attacked Israel in 1948. They took all of what is now known as the West Bank and half of Jerusalem. Because of this, a Palestinian state was never declared. They would keep the land until their defeat in 1967, when Israel would push them back to their current border.

In 1967 Israel gained not only the West Bank from Jordan, but also the Golan Heights from Syria and the Sinai Peninsula from Egypt. Syrian artillery had pounded towns and Kibbutz in northern Israel from the Golan Heights regularly since 1948, and Israel made sure to take as much as they could in 1967 to prevent this from happening any more. There are also stories of soldiers being ordered to take every hill they could until the UN showed up so as to maximize gains after the war in 1973.

Israel's taking of the Sinai desert was also strategic from a defensive point of view. Israelis were now on Egypt's doorstep, holding one side of the Suez Canal and able to threaten Cairo.

Israel relinquished Sinai in the 70's in exchange for peace with Egypt, but today still holds the Golan Heights and the West Bank.

When you hear stolen land, the reference could be to the whole of the West Bank or specifically to land taken by Israelis in the West Bank for Israeli Jewish settlers. The population of the West Bank is almost entirely Arab, but Israel insists on building settlements in the West Bank, on land seized from Palestinians and given to Jews.