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Neural networks is a type of artificial intelligence that attempts to imitate the way a human brain works.

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http://www.webopedia.com/TERM/N/ neural_network.html

To capture the essence of biological neural systems, an artificial neuron is defined as follows: * It receives a number of inputs (either from original data, or from the output of other neurons in the neural network). Each input comes via a connection that has a strength (or weight); these weights correspond to synaptic efficacy in a biological neuron. Each neuron also has a single threshold value. The weighted sum of the inputs is formed, and the threshold subtracted, to compose the activation of the neuron (also known as the post-synaptic potential, or PSP, of the neuron). * The activation signal is passed through an activation function (also known as a transfer function) to produce the output of the neuron.

Neural Networks is the archival journal of the world's three oldest neural modeling societies: the International Neural Network Society (INNS), the European Neural Network Society (ENNS), and the Japanese Neural Network Society (JNNS).

The latest buzz in the Forex world is neural networks, a term taken from the artificial intelligence community. In technical terms, neural networks are data analysis methods that consist of a large number of processing units that are linked together by weighted probabilities. In more simple terms, neural networks are a model loosely resembling the way that the human brain works and learns.
Unlike the traditional data structure, neural networks take in multiple streams of data and output one result. If there's a way to quantify the data, there's a way to add it to the factors being considered in making a prediction. They're often used in Forex market prediction software because the network can be trained to interpret data and draw a conclusion from it.
There are currently dozens of Forex trading platforms on the market that incorporate neural network theory and technology to 'teach' the network your system and let it make predictions and generate buy/sell orders based on it.

Neural networks had been traditionally used to refer to a network or circuit of biological neurons.

The advanced usage of the term often refers to artificial neural networks, which are made up of interconnecting artificial neurons (programming constructs that mimic the properties of biological neurons).

Artificial neural networks are often used for solving artificial intelligence problems.

In finance, it involves the processing of information for accurate financial forecasting and decision making.