Thanks to the work of Camillo Golgi and Santiago Ramon y Cajal, we have been able to understand the functioning of neurons. Between each neuron is a synapse. On either side of this synapse is the presynaptic (axon) and the postsynaptic (dendrite) components. As it goes, information passes from the pre- to the post-synaptic side.
Axon Terminals are capable of releasing various neurotransmitters, which can be used to alter the membrane potential in another dendritic tree.
Arrivign action potentials at the presynaptic cleft can cause depolarization or hyperpolarization of the postsynaptic, based around the released neurotransmitters, and on the postsynaptics ion channels.
The synapse can be considered excitatory or inhibitory based on whether it is depolarizing of hyperpolarizing.Often, single action potentials just aren't good enough to do anything, soi cells incorporate integrate-and-fire model of neuron activity.