The striatum is a single structure in some mammals, but two anatomically distinct nuclei in humans, the caudate and putamen. The two can easily be distinguished as the internal capsule runs between them carrying information to and from the cortex.
The striatum is the main input nucleus for the basal ganglia, receiving information from virtually every cortical area, but particularly the prefrontal, premotor, supplementary motor and primary motor regions. In general, the caudate receives more prefrontal and the putamen more primitive motor information, with the nucleus accumbens (arguably the most ventral portion of the striatum) being thought to have a particular role in emotion and addiction.
The striatum also receives a dopaminergic innervation from the substantia nigra, which alters the balance of the basal ganglia between inhibiting and exciting cortical activity. Reduction in this input in Parkinson's disease causes reduction in the ability to generate movements, whilst degeneration of a group of cells important in allowing inhibition to happen in Huntington's chorea causes an excess of movement. Both diseases can cause changes in cognition analagous to the motor symptoms.
The main output from the striatum is in two streams, 'direct' and 'indirect'. The indirect stream has a net excitatory effect, and passes to the globus pallidus externa (GPe), before progressing to the subthalamic nucleus and then globus pallidus interna (GPi). The direct stream is inhibitory and passes directly to the GPi. The information then travels in a loop by passing to various nuclei of the thalamus, and from there back to the cortex again.