Neurotransmitters are molecules that are the messages sent from the presynaptic neuron to the postsynaptic neuron. There are three major classes of neurotransmitters which all vary in the type of effect and time course on the postsynaptic cell. The most important neurotransmitters are the fast, excitatory neurotransmitters glutamate and acetylcholine. These send strong and immediate excitation from the presynaptic cell to the postsynaptic cell. For example all voluntary muscle contractions happen because of the release of acetylcholine by motor neurons onto muscle cells.
The second type are inhibitory neurotransmitters. These exist because having only interconnected systems made only of excitatory connections have the tendency to be unstable and are subject to seizures, so stability in the nervous system is guaranteed by inhibitory connections using the inhibitory neurotransmitters gamma amino butyric acid and glycine.
The last type are neuromodulators that include both excitatory and inhibitory types. Most neuromodulators are small like somatostatin and enkephalins, but some are organic chemicals called catecholamines such as epinephrine and norepinephrine. The actions of these transmitters are more like hormones because they produce slow but long lasting changes. For example you might be resting after eating and a giant spider lunges at you. That would trigger the release of norepinephrine in this case which is the fight or flight neurotransmitter. Its release shuts down digestion and other internal homeostatic processes if favor of increasing your pulse and blood pressure and diverting blood flow to the muscles in preparation for moving quickly to safety.