A deep feedforward neural network is designed to approximate a function, f(), that maps some set of input variables, x, to an output variable, y. They are called feedforward neural networks because information flows from the input through each successive layer as far as the output, and there are no feedback or recursive loops (models including both forward and backward connections are referred to as recurrent neural networks).
Deep feedforward neural networks are applicable to a wide range of problems, and are particularly useful for applications such as image classification. More generally, feedforward neural networks are useful for prediction and classification where there is a clearly defined outcome (what digit an image contains, whether someone is walking upstairs or walking on a flat surface, the presence/absence of disease...