In reference to Israel, the Green Line is the popular name for what is more correctly known as the "1949 Armistice Line".
The original borders of the state of Israel were determined by the 1947 United Nations partition plan that divided the British Palestine Mandate into a Jewish state and an Arab state. However, following the 1948 War of Independence, Israel annexed a great deal of the territory that had been allocated for an Arab state. The remaining territory was annexed by Jordan and Egypt.
The borders negotiated at the end of the War of Independence form the 1949 Armistice Line. All the territory within this "Green Line" is generally acknowledged by all parties to be "Israel proper", meaning that it is no longer disputed.
In 1967, during a war with Egypt, Jordan, and Syria, Israel conquered additional territory, consisting of the Sinai Peninsula, the Gaza Strip, the Golan Heights, and the West Bank of the Jordan River. This territory, outside the "Green Line", is disputed and has never been considered by the international community as a legitimate part of Israel.
The Sinai peninsula was returned to Egyptian control in 1978, as a condition of the Camp David Accords. The West Bank and Gaza continue to be a focus of negotiation in the Israeli-Palestinian peace process. Syria has stipulated that unconditional return of the Golan Heights is a condition for the beginning of peace negotiations, so little progress has been made in that direction.