It is the combination of the output of all neurons that determines the output of the neural network. In the case of convolutional neural networks (CNNs), the term "feature" is used because it is associated with the feature maps (or activation maps) and filters (or kernels) of the CNN. However, this terminology might not be accurate (because these might not be features in the intuitive sense) and it is used more to interpret the inner workings of the CNN.
After training, the weights of the neural network are fixed (unless you perform online and continual training), so the output of each neuron will be the same given the same input, thus the output of the neural network will also be the same (unless there is some random operation being performed). During training, the weights and thus the output of each neuron (and of the neural network) often change.
The contribution of each neuron to the output of the neural network is determined by the weights of the connections between the neurons, which change during training and can be initialised in different ways, which might affect differently the final weights (after training).
There several ways of visualising the contribution of each neuron to the output of the neural network. See also this article Visualize Features of a Convolutional Neural Network and the paper Visualizing and Understanding Convolutional Networks (2013).