The flow of activation in these network is specified through a weighted summation process. Each neuron sends its current activation any unit is connected to, which is then multiplied by the weight of the connection to the receiving neuron and passed through some squashing function, typical a sigmoid, to introduce nonlinearities (if this were a purely linear process, then additional layers wouldn't matter, since adding two linear combinations together produces another linear combination). Since we typically assume each layer to be completed connected to the next layer, these calculations can be done via multiplying the vector of activations by the weight matrix and then passing all of the results through the squashing function.