The potential or information travels between a pre-synaptic and a post-synaptic neuron. As a reminder, for information, we intend the flow of Na+ and K+ ions between two locations. When the potential arrives at the pre-synaptic neuron terminal, it depolarises the membrane allowing calcium ions (Ca2+) to enter the synapsis. These ions will open the voltage-gated Ca channels between the synapses and promote the synaptic vesicles to fuse to the membrane. The neurotransmitters (contained in the synaptic vesicles) are then released as illustrated.
Now, two events can happen depending on the nature of the neurotransmitter: a new potential can or can not be triggered. If the neurotransmitter is excitatory we will have an EPSP or Excitatory Post Synaptic Potential. The membrane will depolarise promoting the potentials to "pass" from the pre-synaptic to the post-synaptic neuron (physically by lowering the threshold for a new potential to start). On the contrary, if we have an inhibitory neurotransmitter we will have an IPSP or Inhibitory Post Synaptic Potential. Here, the membrane polarises "blocking" the new potential (physically by increasing the threshold for a new potential to start).