GABA (also known as gamma-aminobutyric acid) is the brain's primary inhibitory neurotransmitter; it decreases the likelihood that a particular neuron will fire. It works by opening ion channels that allow chloride ions to flood into the neuron.

How do chloride ions make a neuron less likely to fire? Well, remember that most neurons have a resting potential of about -70 mV--that is, the voltage inside the neuron is 70 mV less that the voltage outside the neuron. If that potential changes to about -60 mV or so, the neuron will fire. Now, excitatory neurotransmitters (like acetylcholine) make positive ions flow into the neuron, raising the potential closer to that -60 mV threshold. If chloride ions (which are negative) flow in, the resting potential will move further away from the threshold (say, down to -90 mV). You'll therefore need lots more excitatory neurotransmitter to get the neuron up to -60.

Benzodiazepines (drugs like Valium and Xanax) are GABA agonists.