For an oversimplified example, to train a neural network to recognize cats and dogs, a developer would present it with an Afghan hound, a beagle, a collie, and a dachshund, while identifying each as an example of a dog. Then the developer would present a Persian cat, a Siamese, and a tabby, while identifying each as an example of a cat. After many iterations, the neural network would converge to recognize the categories of dogs and cats, within some tolerance defined by the data set. Most neural network functions are related to pattern matching and classification. Sometimes a neural network can generalize very well, and sometimes it fails miserably.
Training is still part science and part art.
BP works well for pattern matching and for trend analysis. It is a feed forward network that uses supervised learning to adjust the connection weights. In a feed forward network, the results of each layer are fed to each successive layer. A conventional BP uses three layers of nodes, but it can use more middle layers. The results of the first layer are passed to the next layer.