What is a inhibitory tone when talking about neurons?
Neurons communicate electrochemically. That is, when a signal arrives to a neuron it fires a series of electrical signals, called action potentials.
Action potentials are depolarization events that propagate along the neuronal membrane, down to the neuronal terminal. 
The terminal of a neuron is (with some exceptions) in contact with another neuron, via a structure called synapse.
When the depolarization arrives at the terminal, it allows the entry of calcium, which then mediates the release of a chemical substance, a neurotransmitter into the synaptic space. Finally, neurotransmitters act on the postsynaptic neuron, by binding to specific receptors on its cell membrane and can either stimulate it, in which case the postsynaptic neuron will fire more and release more of its neurotransmitter or inhibit it, in which case the opposite happens.

The textbook example of a stimulatory neurotransmitter is glutamate, and the inhibitory one is GABA1.

In various areas of the brain certain neurons are constantly receiving inputs from GABAergic afferents. This means that those neurons are constantly receiving a GABA stimulus that inhibits them, and are thus under a constant inhibitory tone. This will prevent their firing until a sufficiently potent stimulatory stimulus arrives or until the inhibitory tone is somehow released (for instance if the inhibitory GABAergic afferents are themselves inhibited by some of their own afferents). 



1note that this is not always true: GABA can also be stimulatory in various situations