In most instances of natural neuron inhibition GABA is the inhibitory transmitter.   GABA has the specific effect of opening anion channels in nerves, allowing large numbers of chloride ions to diffuse into the terminal fibril.  the negative charges of these ions cancel much of the excitatory effect of the positively charged sodium ions that enter the terminal fibril when as action potential arrives.  The cell is thus become hyperpolarized and the action potential in these neuron fibrils becomes greatly reduced.