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A neural network is designed to simulate a set of neurons, usually connected by synapses. Each neuron makes a simple decision based on its other input synapses, and places the decision on its output synapses. This model mimics the behavior of a brain, and is considered vital to create a true learning system, though modern computers (barring super-computers) do not have the computational resources to execute a neural network with a sufficient number of nodes to be useful (you would need at least a few million neurons firing in unison to be useful).

Artificial Intelligence, of course, is software that is designed to pretend like its a living, thinking creature. Older implementations were not learning systems, but rather would take input and offer a conditioned response provided by the programmer ahead of time. These systems seemed to be highly intelligent, so long as you did not leave its realm of preplanned responses. Newer AI systems learn by interacting with the user (for example, remembering their favorite color or music artist), and can sometimes even figure out correlated data based on this information.

However, current AI systems tend to still have limited spheres of knowledge, and without external learning sources, can not make any intelligent responses or decisions outside this realm of information. The missing component, of course, is a system that is capable of learning information and incorporating what it learns into its current knowledge base. Neural networks hold the promise of bridging this gap in the "learning curve" that AI systems have by allowing the AI to actually learn topics that were not covered during its original "training" or "programming."

The relationship between these two technologies could be said to be symbiotic in nature; both of these can be implemented without the other (i.e. a NN could be used inside a coffee maker for some advanced coffee-making logic, and an AI can certainly use other sources of information to make valid responses), but the combination of the two would allow for a more realistic AI that would be capable of learning data by making correlations between seemingly unrelated data (which is how humans learn, coincidentally).

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