Final answer:
The space between a neuron and a target cell is called a synapse, which encompasses a synaptic cleft where neurotransmitters facilitate communication.
Step-by-step explanation:
The space between a neuron and a target cell is named the synapse. A synapse consists of a gap known as the synaptic cleft, where neurotransmitters are released from the presynaptic neuron and travel across to bind to receptors on the postsynaptic neuron or target cell, thus facilitating intercellular communication. Synaptic transmission includes both electrical and chemical processes and is critical for the functioning of the nervous system.