The National Missile Defense Shield is a system designed to protect the US and it's interests from foreign nuclear threats. Through such means as antiballistic missiles and other technologies, the goal is to stop the threat before it is able to deliver its payload and cause damage. It's an extremely controversial technology, and is in many ways, a relic of a different time.
In order to understand the current desire for a national missile defense shield, its best to start at the beginning of research into the field. During the height of the cold war, the US and the Soviet Union were in a nuclear arms race. Each country was trying to maintain the upper hand in the policy of mutually assured destruction - that uneasy peace caused by knowing that if either side struck, both sides would end up destroyed. Antiballistic missiles, or anti-missile missiles, were supposed to be what gave the US the upper hand.
Instead of worrying about not starting a nuclear war, the US would simply shoot down missiles as they come in. There would no longer be a need to fear "them" sending over missles. US policy makers would have the upper hand; they could set much more wide-ranging policies without worrying about the other side starting a nuclear war. After all, if you can shoot down all their missiles you can theoretically strike with impunity.
Unfortunately, real world practices differ from theoretical applications. Shortly after the realization that such a system was possible, engineers and politicians on both sides began wracking their brains trying to determine both how to implement the technology for their side, and circumvent the technology the other side uses. Ideas were thrown back and forth as to how to best utilize the technology, when the frightening yet simple way around this technology was discovered. Just flood them with missiles.
It's almost mind-numbing how low tech the way around this technology is. Instead of sending out 100 missiles as a first wave, just send out two hundred, or five hundred, or however many it takes to overload the other end's defense. Sure, a vast majority of the missiles will be shot down, but throw enough of them at the enemy, and at least a few of them are bound to get through. This meant that both sides were right back where they started. Just build more missiles, and try to break through their defenses.
Obviously, policy makers on both sides saw how this could lead to disaster, antiballistic missiles didn't lessen the vulnerability of either side. In fact, all they did was increase already strained relations between to behemoths. High level leaders on both sides met and hammered out a treaty banning antiballistic missiles. After all, World War III was, and still is, something to be avoided.
Fast forward to the present day. The "evil empire" has fallen, so you'd think that there would no longer be any consideration for a missile defense system. When the other major nuclear power has trouble just paying their electric bills, it is doubtful that they are going to wage war anytime soon.
That instability, however has lead to the threat of a so-called rogue state, such as Iran, North Korea, or China getting a hold of a nuclear device and detonating it in a major US city.
The theory goes that a rogue state or terrorist group will purchase a nuclear device on the black market and build a missile-based delivery system to attack a US city. The missile defense system is supposed to stop an attack such as this because unlike the former Soviet Union, most rogue nations won't have more than a handful of nuclear weapons. Thus, any attack could be easily handled with a relatively small number of missiles.
Unfortunately, that's not how a rogue state would probably use such a device. For starters, creating an ICBM is both technically and financially difficult. Exceedingly few entities are able to afford creation of such a delivery system, and most of them have extensive such ties to the US that an attack would mean extensive sociopolitical ramifications for themselves as well. Additionally, many of the materials required to create such a system are closely monitored. It's extremely doubtful that even a well-financed organization would be able to procure the materials necessary for launching a warhead without facing close scrutiny by external parties.
At this point, many supporters of a Missile Defense Shield are probably saying to themself "but the US is such a big target, They'd try at least something to deliver a warhead". I agree with that they would try something; the US is disliked by a great number of parties, some of which would try a nuclear attack if they were able to. But, a missile is just too high tech, and too error-prone to be considered. Any organization trying to attack the US would be much more likely to do so with a more low-tech approach, such as through a so-called suitcase nuke, or through a much more low key mode of transportation, such as a boat or airplane. Who needs a missile when the alternatives are much cheaper and much more effective?
In conclusion, like so many ideas, a National Missile Defense Shield looks brilliant on paper, but fails in the real world. When first proposed, it failed due to the arms race; the other side would simply make enough missiles to overwhelm the defenses. The current proposal fails for an equally simple reason - using a high tech device to deliver a weapon is not the way a rogue group would operate. As was shown on September 11, 2001, groups will attempt to subvert the system from methods which place a low emphasis on technology. Any message they want to send would be done so with a method which minimizes the threat of detection, and a missile is just too flashy and too failure-prone. Instead of worrying about a non-existent threat, much more time and effort needs to be placed in dealing with the problems that truly do exist through such tried and true methods as communication, diplomacy, and compromise. Playing a multi-billion dollar version of missile command isn't going to help.