In the nervous system there are primarily two ways of propagating signals. By far the most common method of intracellular signal propagation is the action potential. The dendrites of neurons contain ionotropic (aka ligand-gated ion channel) and metabotropic neurotransmitter receptors that bind chemical neurotransmitters. At ionotropic receptors, these chemical neurotransmitters cause quick changes in ion flux into or out of the cell. The resulting internal voltage change in the dendrites is propagated towards the cell body and axon hillock, where a large concentration of voltage-gated ion channels typically exists. If some voltage threshold is met, voltage gated sodium channels open up, letting in a critical charge of sodium, and the positive current propagates down the axon towards the presynaptic axon terminal. This action potential leads to neurotransmitter vesicular release at in this terminal.
While action potentials are the typical means of signal propagation in the nervous system, some sensory neurons use graded potentials to trigger vesicular release. These cells are typically short enough that regenerative action potentials aren't needed to cause a large enough voltage change at the presynaptic terminal. For example, photoreceptor cells in the eye produce graded potentials in response to light, and these graded potentials can directly lead to neurotransmitter release.