Nuclear proliferation is a major issue in the world today. It is particularly relevant at the moment with the worries about Iran and whether they are trying to get nuclear weapons. Let us look at why this is so.
Nuclear proliferation is generally caused by the fact that countries want to be secure and to be powerful. It is also caused to some degree by the fact that it is difficult to prevent. Countries see nuclear weapons as a path to security and power. They see, for example, how the international community cannot challenge North Korea when it does things like sinking South Korean ships. The fact that the North Koreans have nuclear weapons makes them, in a sense, untouchable. Countries like Iran see this and want to have that sort of protection as well.
Countries also see that it seems to be impossible to prevent proliferation and are therefore not deterred from seeking weapons. They see, for example, that countries like China and Russia will typically not help with international efforts to deter countries from seeking nuclear weapons. Therefore, they figure that they will not be punished in any significant way for participating in proliferation activities.
The major consequence of proliferation is that it makes for a less stable world. There are at least two ways in which this is true. One way is the North Korean way. The fact that they have nuclear weapons allows them to do all sorts of provocative things that destabilize their region and make for a permanent sense of crisis. A second way is the Iranian way. As countries seek to get nuclear weapons, they cause concern for those around them. Those around them may seek to get their own nuclear weapons. They may consider preemptive military action, as Israel is considering taking against Iran. In other words, they can cause instability in their region as rival countries consider steps they might take to prevent their rival from getting nuclear weapons or from being the only nuclear power in the region.
Proliferation happens, then, because there seem to be more benefits than costs to it for some countries. When it happens, it tends to cause instability in the area of the country that is trying to get nuclear weapons.