Egyptian troops with banners calling for the defeat of Israel and death to the Jews
The Six-Day War — the third major Arab-Israeli conflict — was in a sense a continuation of the first two wars. Broadly speaking, the causes of the fighting in 1967 overlapped with the causes of fighting in 1948 (Arab rejection of Israel) and 1956 (continued rejectionism and an Egyptian blockade of shipping to Israel). See here for more.
Specifically, the war stemmed from Egypt's decision to expel United Nations troops from the Sinai peninsula and blockade Israel's port of Eilat, under international law a casus belli, or act of war, in addition to belligerent Arab threats to destroy Israel. Much of the above could be traced to Soviet meddling and misinformation.
Select from the left-hand menu for details about the precursors to the Six-Day War.