The Basal Ganglia are a collection of neuron's found in the center of the brain (see picture to the left for the location of the Basal Ganglia). As you can see, this area is located well within the middle of the brain. The Basal Ganglia seem to be chiefly involved in motor processes. That is why disorders of them, such as Parkinson's or Huntington's disease leads to problems with movement.
The Basal Ganglia do not directly control movement, areas of the cortex do that. Instead, they seem to exert an influence which picks out the correct type of movement. It helps if you think of the Basal Ganglia as a policeman at an intersection. Just like there are a lot of different cars, each needing to go its own way. There are a lot of different motor impulses in our brain, often going against one another. Like the policeman, the Basal Ganglia keeps all these impulses working in an orderly matter. It is only with this control that we can coordinate all of our complicated movements.
As you can see in the diagram bellow, the connections which the Basal Ganglia make are very complicated. The Basal Ganglia itself is made up of the the striatum, which is also called the caudate and putamen, and the globus pallidus. The major inputs that it receives are from the cortex, which contains higher levels of thinking and the substantia nigra, an area in the midbrain that uses the neurotransmitter dopamine. It's major output is to the thalamus, where it has an overall inhibitory effect on movement.
If these seems really complicated don't worry. The important thing to remember is that the basal ganglia receives inputs from a lot for different areas and that it's major output reduces the amount of motor activity. Damage to the Basal Ganglia and the areas from which it receives information are gong to cause either a decrease or increase in movement, depending on whether the damage increases or decreases the overall activity of the system.