When an action potential arrives at the end of a presynaptic neurone, it causes the uptake of calcium ions through ion channels in the wall of the synapse. This influx of calcium ions causes vessicles of acetyl choline found in the presynaptic neruone to fuse with the presynaptic membrane, releasing its contents into the synaptic cleft.
Acetyl choline diffuses across the cleft and binds to receptors in the postsynaptic membrane, causing the opening of sodium channels in the postsynaptic neurone. This influx of sodium ions depolarises the membrane and initiates an action potential in this neurone, allowing the continued transmission of the signal.