A synapse is a point between two different neurons: the one sending the signal is called a presynaptic neuron and the one receiving the signal is called a postsynaptic neuron.
The picture below demonstrates the synaptic cleft between two neurons. The process which ultimately triggers the release of neurotransmitters is similar to someone receiving a phone call: you wouldn’t know the phone was ringing unless you could either hear it through a ringtone or feel it (through a vibration), would you?
The phone would ring and the receiver would most likely answer after someone else picked up their phone, received a dial tone and dialled the appropriate number: similar processes are involved with synapes.
The first step of the process within the synaptic cleft starts with a signal arriving through the axon. This is similar to a telephone line: it sends the signal to the other phone. The increase in electrical potential opens the voltage-dependent gates which allow calcium (Ca2+) into the cells.
Once the calcium has been released into the axon, it channels down through the axon terminal and binds itself to a sensor protein. This complex of Ca2+ and the sensor protein makes the synaptic vesicles (filled with neurotransmitter) fuse with the edge of the synaptic cleft and subsequently release their contents into the synaptic cleft.
A pictographic representation of what I just talked about can be found below. I know this process can be tricky to understand (when I studied it, it took me a few read-throughs to fully understand it), so don’t feel ashamed if you’re scratching your head after reading it through the first time. Unfortunately, I couldn’t make the picture any larger, so if you’re having trouble reading it, just click on the image and it should fill up the screen.