What is the role of calcium in synaptic activity?

In a classic synapse, calcium's main role is to trigger the release of chemicals (called neurotransmitters) from the presynaptic neuron. How calcium does this is well established and is achieved through voltage-gated calcium channels located on the membrane of the presynaptic terminal. These channels open in response to membrane depolarization, the type of signal carried by an action potential.

The whole process goes something like this: When an action potential arrives at the presynaptic terminal, it depolarizes the membrane sufficiently to open voltage-gated calcium channels. The calcium gradient across the membrane is such that when these channels open, an inward calcium current is produced, with calcium rapidly entering the cell. Calcium is rapidly bound by a presynaptic intracellular protein called synaptotagmin. Synaptotagmin is considered a calcium sensor that triggers a host of downstream events. Ultimately, synaptotagmin activation results in the fusion of neurotransmitter vesicles with the presynaptic membrane. These vesicles fuse with the membrane through interactions between v- and t-snares (the "v" and "t" stand for "vesicular" and "target", respectively) causing the release of neurotransmitters into the space between the pre- and postsynaptic terminal. Individual molecules of neurotransmitter diffuse across this space, called the synaptic cleft, and ultimately bind to receptors on the postsynaptic cell membrane.

Since calcium triggers the conversion of an electrical signal (the action potential) into a chemical one (the release of neurotransmitters), calcium can be thought of as the trigger for electrochemical transduction (the term literally means the conversion of electrical into chemical information).