What happens when an impulse reaches the end of the presynaptic nueron?

The pre-synaptic neuron repolarizes.

The change in polarity triggers the rapid influx of calcium into the cell. This causes vesicles to bind to the membrane and release neurotransmitters into the synapse. These neurotransmitters then bind to receptors on the surface of the postsynaptic neuron, which open ion channels. The ions may either contribute to exciting or inhibiting an action potential in the postsynaptic neuron.
There is also a less common type of synapse in which the action potential is transmitted directly from one neuron to another through gap junctions.