In a Feed-Forward NN, each neuron has its own set of parameters that affect it and different neurons have distinct set of parameters. Each parameter is used exactly once.

In contrast, in CNNs using the kernel convolution means that this kernel affects several output elements at once. This is because a feature detector (such as a vertical edge detector) that is useful in one part of the image, is probably useful in another part of the image. The main advantage is that it decreases the memory requirement significantly.

As you can see in the example arrows of the same color indicate the same parameters.