Perhaps a more cautious, but accurate assertion is 'Your brain is
like a supercomputer'. Throughout history
thinking people have tried to understand the nature of the thing between their ears and have, quite naturally, drawn analogies with whatever technology is around at the time.
Mechanical engines,
telegraph networks and
early computers have had their moment. Computer networks represent the current state of the art and so we compare them to the only thing we know that beats them hands down -- our brains.
The 'computer' in my head has trouble remembering telephone numbers. It's also quite slow at doing simple arithmetic. Simple, cheap computers are much better at this and make far fewer mistakes. Does this represent a design flaw in the human brain? Not really. Evolution has dictated that remembering faces and abstract reasoning are far more important.
Evolution produced the brain, and it shows. The brain is composed of a series of layers ballooning out from the top of the spinal column, each one a later extension/patch/upgrade to those before which adds more abstract capabilities. Each layer is made up from groups of your basic neuron. Each neuron may take several milliseconds to fire, in which time a supercomputer may have processed many millions of instructions. However, since very many neurons can fire at a time, the brain has inherent massive parallelism and this is the key to its awesome power.
Supercomputers have been built with large-scale parallelism (see Daniel Hillis) and Neural Networks have been knocking around for ages. IMNSHO, wherever this research goes will be closer to brains than today's supercomputers, not just in power but in nature.