The function of the active zone is to ensure that neurotransmitters can be reliably released in a specific location of a neuron and only released when the neuron fires an action potential.
As an action potential propagates down an axon it reaches the axon terminal called the presynaptic bouton.  In the presynaptic bouton, the action potential activates calcium channels (VDCCs) that cause a local influx of calcium.  The increase in calcium is detected by proteins in the active zone and forces vesicles containing neurotransmitter to fuse with the membrane.  This fusion of the vesicles with the membrane releases the neurotransmitters into the synaptic cleft (space between the presynaptic bouton and the postsynaptic membrane).  The neurotransmitters then diffuse across the cleft and bind to ligand gated ion channels and G-protein coupled receptors on the postsynaptic membrane.  The binding of neurotransmitters to the postsynaptic receptors then induces a change in the postsynaptic neuron.  The process of releasing neurotransmitters and binding to the postsynaptic receptors to cause a change in the postsynaptic neuron is called neurotransmission.