Final answer:
A neuromodulator is the substance that influences neuronal activity and originates from non-synaptic sites, working more slowly than neurotransmitters and having a broader effect on neural circuitry.
Step-by-step explanation:
The substance that influences neuronal activity and originates from non-synaptic sites is known as a neuromodulator. Unlike neurotransmitters, which act directly and rapidly at synaptic junctions, neuromodulators tend to work more slowly and can influence a number of neurons at once. Neuromodulators may come from various sources within the brain and, upon release, they modify the effects of neurotransmitters. This can either amplify or diminish the strength of synaptic transmission and thus affect the neuronal circuitry on a broader scale. This mode of action is different from neurotransmitters, which are usually involved in fast and direct communication between neurons.