In October 1973, the Arab members of OPEC, and Egypt and Syria, announced an oil embargo on the United States (and all other nations that supported Israel) in response to decision to supply the Israeli army during the Yom Kippur War. This caused oil prices to skyrocket.
This oil crisis caused shifts, rifts and strains in alliances between other countries. With the US actions seen as initiating the oil embargo, the long-term possibility of embargo-related high oil prices, disrupted supply and recession, created a strong rift within NATO; both European nations and Japan sought to disassociate themselves from the US Middle East policy, as they imported most of their oil from the Middle East. Former cooperation between the USSR and Arabic countries became a more adversarial relationship as the Soviet Union increased oil production and export to take advantage of the supply problems in the West created by OPEC's production reductions. It caused the Cold War policies of the Nixon administration to suffered a major blow as the challenge to U.S. hegemony coming from the Third World became evident with the oil crisis.
The event was unlikely to start a nuclear war. Countries wanted have oil, not destroy their oil sources.