In the nervous system, a synapse is a structure that permits a neuron to pass an electrical or chemical signal to another cell (neural or otherwise).
There are two fundamentally different types of synapses: - In a chemical synapse, the presynaptic neuron releases a chemical called a neurotransmitter that binds to receptors located in the postsynaptic cell, usually embedded in the plasma membrane. The neurotransmitter may initiate an electrical response or a secondary messenger pathway that may either excite or inhibit the postsynaptic neuron.
Further, there is a type of signaling called “ephatic coupling”, wherein neurons become coupled not through a direct synapse, but through proximity (sharing ions in chemical synapses, and via electric fields in electical synapses). This looks (to me) to be what changes a neural network from a linear circuit into some far more “random”.