In the easiest example of a neuron in a artificial neural network, you take an image, you multiply every pixel by some weight, and you apply a very simple non linear transformation at the end. Any transformation is fine, but usually they are pretty trivial. Then you mix and match these neurons to create a neural network. The more complex the task, the more additional operations are added.

In our brain, a neuron binds some neurotransmitters that trigger a electrical signal, this electrical signal is modulated and finally triggers the release of a certain quantity of certain neurotransmitters on the other extreme of the neuron. Detailed, quantitative mechanisms are still not known. These neurons are put together in an extremely complex neural network, details of which are still unknown.

Artificial neural network started as an extremely coarse simulation of real neural networks. Just toy models to explain the concept. Since then, they diverged, evolving in a direction completely unrelated to real neural network, becoming their own thing.