The electrical signals in our nervous system are analog, not digital.

Analog means it operates with some form of continuity. Your nervous system (which your brain, and thus, your neurons, is part of) is operates thru the passing of continuous electrical signals.

Symbolic just means that is serves as a representation. I.e. the "neuron" in an ANN is not a real neuron. It just symbolizes one.

Neural networks are basically groups of containers for series of mathematical operations, both within the container and across layers of containers. "Symbolic" is referring to the fact that early researchers decided to call these containers "neurons", to symbolize the way biological neurons in our brains share "information" with each other (i.e. a network of neurons). ANNs are static in the sense that once you define the architecture (# of layers, neurons per layer, layer-to-layer connections) this architecture does not change. Your brain, however, does transform itself as you age and learn new things, hence it is dynamic.