In a bi-polar or tri-polar world, the concept of Mutually Assured Destruction makes a lot of sense. With three nuclear power blocs (the West, led by the US, the Soviet Union and China) each capable of destroying each other should nuclear conflict arise, relative peace was maintained by guaranteeing the absolute destruction of any bloc that initiated nuclear war upon one or both of the other blocs. For this scenario to work it was necessary that no bloc be able to defend against nuclear strikes, and that each bloc have retaliatory capabilities that would survive a first strike. Any strike made by one bloc would completely destroy the target's society, but also trigger a retaliating strike that would completely destroy the agressor bloc.
This scenario rendered large scale war between the blocs suicidal. To attack one of the other blocs was to destroy your own. When the balance was firm, tensions could remain low. When missile defence technologies developed they destabilized the balance by making survival of a first strike possible. Worse, missile defence technology also protected against a retaliatory response, making a first strike possible. It is claimed by some that the apparent capability of the US to develop an operation missile defence system (Star Wars) was one of the main contributors to the collapse of the Soviet Union - they could no longer compete in the arms race nor protect themselves. This lead to the short lived era of the single superpower, the United States, the so-called "End of History", and a much more interesting time in foreign affairs and statecraft.
If large scale war was avoided during the Cold War, proxy wars were not. Proxy wars, fought in third world countries, usually with indigenous troops, could exchange power and influence along the margins, but never threatened the existence of any bloc. This made them possible, and possibility was, from time to time, advantageous to all players. With the end of the capitalist/communist power struggle the small wars continued, but they were proxies for different players as the world transformed itself into a multi-polar one.
In Europe the collapse of the Soviet Union occassioned the collapse of the Warsaw Pact, and expansion of Nato. This, coupled with the emergence of independent countries previously subsumed within the Soviet Union created new power structures from, to re-utilize the words of Churchill, from Stettin on the Baltic to Trieste on the Adriatic". A shooting war erupted as Yugoslavia broke up, along with smaller conflicts in Chechnya and Georgia.
In the Middle East the dominant theme has been the rise of aggressive Islamism, combined with historical territorial ambitions. Iran has sought to extend it's influence across the neighbouring Arab world while Turkey has moved away from Western oriented secularism and toward a neo-Ottoman vision. First in the game, Iran has established proxies in Lebanon, Syria and Gaza, and has fought the US (through the IRGC) directly in Iraq and Afghanistan. Israel has been in a state of low level war for decades, and the Arab Spring has created more uncertainty, conflict and at times chaos.
This change has occurred while the nuclear club remained relatively stable. The only true wild card was Pakistan, who possessed not only the bomb, but also an continually unstable government. Even it was stuck in a paradigm of staring down India (which must be estatic that it never found itself in the unenviable position of occupying a conquered Pakistan). The conflicts of the late 20th and early 21st century were small potatos, and did not seem to threaten the established order, at least not substantially. It did not make a great deal of difference if Yugoslavia broke up, or if the Ukraine or Georgia left the Soviet Union, and the Arabs and Israelis fought perpetually anyway.
The important development, of course, has been the quest of Iran for nuclear capabilities. It is important because it makes clear that nuclear weapons make conventional war possible, provided the war is within reason. When Iran gets the bomb it will be able to destroy Israel, which is a huge blow for Islamists. Israel may destroy Iran, leading some to believe that a mini-MAD applies, but IRan has stated, in a very destabilizing fashion, that in a nuclear exchange Israel would be destroyed while Islam would only be hurt. The implication is that Iran is not worried about Iran, but about Islam, that Iran will sacrifice Iran for Islam, and therefore, since Israel can only destroy Iran, but not Islam, there is no MAD. Iran is free to destroy Israel whenever it wants. This is a scary scenario, and it serves it's purpose, but it is not realistic. The purpose of the implied ability to destroy Israel is to distract.
Iran's real goal is to become the regional power, and control the Middle East. It currently competes with Saudi Arabia and Turkey. It has engaged in a terrible war with Iraq, and has fought the US in both Iraw and Afghanistan. It maintains proxies to attack Israel, and reportedly has deployed IRGC personnel in both Gaza and Lebanon. After more than 30 years of struggle it has not achieved it's historic goal (historic if you believe that actors chnge but geography remains the same).
A nuclear weapon allows Iran to make use of it's conventional forces in the region. It can clash with Turkey with conventional means. It can lose to Turkey without risking invasion because it will be able to threaten nuclear force against Ankara. No other nuclear power could stop Iran, not the US, not Russia and not China, if Iran decided to engage in conventional warfare with a neighbour. By intervening conventionally the US could force Iran out of, for example, Iraq, or Afghanistan, but it would require a massive conventional force that would be unable to actually topple the Iranian regime or invade the country without running the risk of some sort of nuclear escalation.
Iran realizes this, and realized it long before any other country did (where was the game of chess invented, anyway?) It recognized that the major powers of the world were like armed men who put their weapons away in order to sort things out with fisticuffs, understanding that the fight was limited to a non-existential result- the fact that the major powers didn't recognize that arrangement didn't mean it did not exist. Anyone with nuclear weapons has the ability to wage conventional warfare on a limited basis. Iran has demonstrated that it will sacrifice millions in combat, and now it's getting the bomb, which will allow it to use it's conventional weapons to further it's regional aims.
Unless the United States, Russia or China is willing to get into a conventional war in the Middle East, Iran will have its way. No great power will start a nuclear war over Israel, let alone Syria, Iraq, Jordan or Saudi Arabia.