Today, computers are greatly evolved machines. They run at blindingly fast processor speeds of around 3 GHz. That too with multiple cores. They can do calculations, perform mathematical manipulations, forecast weather, guide missles with pin point accuracy. Something which humans simply cannot do at such high speeds.
But there are tasks that humans can do really fast. And today's computers can't even compete with humans. Tell a human to drive a car. He'll do all the complex "calculations" inside his head, and drive the car perfectly. But to train a computer to drive a car is a mammoth challenge in itself. Infact, the US Military organizes a competition to create such a computer every year (called the DARPA challenge). And these computers don't run in traffic jammed lanes... they move in relatively free and wide tracks.
Another example would be vision, or audio recognition. Humans, or even animals, can easily recognize patterns. Doesn't you dog come to you when you call out its name?
So, where does the semiconductor technology fail?
No one knows the answer for sure as of now. But a possible answer might be, because humans do "calculations" in a fundamentally different way than computers do.
Computers are made up of transistors, chips, etc. Humans, on the other hand, use their brains.
The brain is a network of neurons. A lot of them. Billions of them. And their interconnections is what makes the brain so powerful at such cognition tasks.
So the scientists and experimenters decided to try and simulate the brain artificially. No they did not use billions of neurons. They used only a few. Maybe a few hundreds, or maybe a couple of thousands. And they found that they could actually do tasks they couldn't with proper "computer programs".
They could recognize handwritten characters, interpret vision, without using a 3 GHz + 12GB RAM computer! This was amazing. They HAD to name this something!! Because this was based on the brain's neural interconnection, they decided to call the thing a "Neural Network".
And the best thing about these neural networks is their simplicity. You don't need to dabble with probability or differential equations just to recognize characters. Simple mathematical operations are sufficient to make the neural network "learn" complex tasks.
One reminder though. Biology still does not know exactly what goes on in the brain. The artificial "brains" or neural networks created are only crude approximations of how the brain actually functions. Once biology unlocks the secrets of how the brain actually works, humans just might be able to combine the computational speed of computers and the ability of neural networks to do complex tasks.