The gap where an electrical signal jumps from one neuron to another is called the synaptic cleft. This is a closeup of the cleft between one neuron and another. Since the impulse cannot cross a gap as electricity, it crosses as a "message" by means of chemical messengers called neurotransmitters.
This animation shows the action of a neurotransmitter called GABA, which acts to quiet electrical activity in parts of the brain. The GABA is produced in one neuron, here the one shown at the top. It is stored in packages called vesicles that move to the cell membrane and release the GABA into the cleft. The GABA crosses the gap between the neurons, and then binds to receiver sites, or receptors, on the neighboring neuron, shown at the bottom.
When GABA occupies a receptor, it decreases the neuron's electrical activity. (That is, the neuron's electrical activity "quiets down.") After a while, the GABA comes off the receptor and is removed from the synapse by reuptake pumps that return it to the first neuron.