Training for unsupervised Kohonen networks requires that the weights leading to the winning neuron are adjusted after each pattern passes through the network. However, the winning neuron needs to have a positive influence on the neurons which physically surround it, i.e., its neuron neighbors. Therefore, the weights for the neurons in the neighborhood around the winning neuron are changed during training, too.
The neighborhood size is variable, starting off fairly large (sometimes even close to the number of neurons in the output layer) and decreasing with learning until during the last training events the neighborhood is zero. By then only the winning neuron's weights are changed.
Neighborhood size is set when designing the Kohonen architecture.